{"id":20203,"date":"2024-04-15T05:49:45","date_gmt":"2024-04-15T05:49:45","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20203"},"modified":"2024-04-15T05:49:45","modified_gmt":"2024-04-15T05:49:45","slug":"for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/","title":{"rendered":"For a small value of h, the Taylor series expansion for f(x + h) is A. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] B. \\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] C. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] D. \\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]"},"content":{"rendered":"

[amp_mcq option1=”\\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]” option2=”\\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]” option3=”\\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]” option4=”\\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]” correct=”option1″]<\/p>\n

The correct answer is:<\/p>\n

\n

C. [{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty ]<\/p>\n<\/blockquote>\n

The Taylor series expansion for a function $f$ about a point $x$ is given by:<\/p>\n

$$f(x+h) = f(x) + hf'(x) + \\frac{h^2}{2!}f”(x) + \\frac{h^3}{3!}f”'(x) + \\cdots$$<\/p>\n

The first term, $f(x)$, is the value of the function at the point $x$. The second term, $hf'(x)$, is the product of the function value and the change in $x$. The third term, $\\frac{h^2}{2!}f”(x)$, is the product of the change in $x$ and the second derivative of the function. The fourth term, $\\frac{h^3}{3!}f”'(x)$, is the product of the change in $x$ and the third derivative of the function. And so on.<\/p>\n

The Taylor series expansion is a way of approximating the value of a function at a point $x+h$ by using the values of the function and its derivatives at the point $x$. The more terms of the series that are included, the more accurate the approximation will be.<\/p>\n

In the case of the Taylor series expansion for $f(x+h)$, the first term is the value of the function at the point $x$. The second term is the product of the function value and the change in $x$. The third term is the product of the change in $x$ and the second derivative of the function. The fourth term is the product of the change in $x$ and the third derivative of the function. And so on.<\/p>\n

The Taylor series expansion is a powerful tool that can be used to approximate the value of a function at a point that is not easily evaluated. It can also be used to find the derivatives of a function.<\/p>\n","protected":false},"excerpt":{"rendered":"

[amp_mcq option1=”\\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]” option2=”\\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]” option3=”\\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]” … <\/p>\n

Detailed SolutionFor a small value of h, the Taylor series expansion for f(x + h) is A. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] B. \\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] C. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] D. \\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"class_list":["post-20203","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\nFor a small value of h, the Taylor series expansion for f(x + h) is A. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] B. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] C. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] D. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\]<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"For a small value of h, the Taylor series expansion for f(x + h) is A. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] B. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] C. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] D. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\]\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=”[{text{f}}left( {text{x}} right) + {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{2}{text{f}}”left( {text{x}} right) + frac{{{{text{h}}^3}}}{3}{text{f}}”left( {text{x}} right) + ,…,infty ]” option2=”[{text{f}}left( {text{x}} right) – {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{{2!}}{text{f}}”left( {text{x}} right) – frac{{{{text{h}}^3}}}{{3!}}{text{f}}”left( {text{x}} right) + ,…,infty ]” option3=”[{text{f}}left( {text{x}} right) + {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{{2!}}{text{f}}”left( {text{x}} right) + frac{{{{text{h}}^3}}}{{3!}}{text{f}}”left( {text{x}} right) + ,…,infty ]” ... Detailed SolutionFor a small value of h, the Taylor series expansion for f(x + h) is A. [{text{f}}left( {text{x}} right) + {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{2}{text{f}}”left( {text{x}} right) + frac{{{{text{h}}^3}}}{3}{text{f}}”left( {text{x}} right) + ,…,infty ] B. [{text{f}}left( {text{x}} right) – {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{{2!}}{text{f}}”left( {text{x}} right) – frac{{{{text{h}}^3}}}{{3!}}{text{f}}”left( {text{x}} right) + ,…,infty ] C. [{text{f}}left( {text{x}} right) + {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{{2!}}{text{f}}”left( {text{x}} right) + frac{{{{text{h}}^3}}}{{3!}}{text{f}}”left( {text{x}} right) + ,…,infty ] D. [{text{f}}left( {text{x}} right) – {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{2}{text{f}}”left( {text{x}} right) – frac{{{{text{h}}^3}}}{3}{text{f}}”left( {text{x}} right) + ,…,infty ]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:49:45+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"For a small value of h, the Taylor series expansion for f(x + h) is A. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] B. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] C. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] D. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\]","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/","og_locale":"en_US","og_type":"article","og_title":"For a small value of h, the Taylor series expansion for f(x + h) is A. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] B. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] C. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] D. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\]","og_description":"[amp_mcq option1=”[{text{f}}left( {text{x}} right) + {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{2}{text{f}}”left( {text{x}} right) + frac{{{{text{h}}^3}}}{3}{text{f}}”left( {text{x}} right) + ,…,infty ]” option2=”[{text{f}}left( {text{x}} right) – {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{{2!}}{text{f}}”left( {text{x}} right) – frac{{{{text{h}}^3}}}{{3!}}{text{f}}”left( {text{x}} right) + ,…,infty ]” option3=”[{text{f}}left( {text{x}} right) + {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{{2!}}{text{f}}”left( {text{x}} right) + frac{{{{text{h}}^3}}}{{3!}}{text{f}}”left( {text{x}} right) + ,…,infty ]” ... Detailed SolutionFor a small value of h, the Taylor series expansion for f(x + h) is A. [{text{f}}left( {text{x}} right) + {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{2}{text{f}}”left( {text{x}} right) + frac{{{{text{h}}^3}}}{3}{text{f}}”left( {text{x}} right) + ,…,infty ] B. [{text{f}}left( {text{x}} right) – {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{{2!}}{text{f}}”left( {text{x}} right) – frac{{{{text{h}}^3}}}{{3!}}{text{f}}”left( {text{x}} right) + ,…,infty ] C. [{text{f}}left( {text{x}} right) + {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{{2!}}{text{f}}”left( {text{x}} right) + frac{{{{text{h}}^3}}}{{3!}}{text{f}}”left( {text{x}} right) + ,…,infty ] D. [{text{f}}left( {text{x}} right) – {text{hf}}’left( {text{x}} right) + frac{{{{text{h}}^2}}}{2}{text{f}}”left( {text{x}} right) – frac{{{{text{h}}^3}}}{3}{text{f}}”left( {text{x}} right) + ,…,infty ]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T05:49:45+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/","url":"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/","name":"For a small value of h, the Taylor series expansion for f(x + h) is A. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] B. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] C. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\] D. \\[{\\text{f}}\\left( {\\text{x}} \\right) - {\\text{hf}}'\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}''\\left( {\\text{x}} \\right) - \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}''\\left( {\\text{x}} \\right) + \\,...\\,\\infty \\]","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T05:49:45+00:00","dateModified":"2024-04-15T05:49:45+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/for-a-small-value-of-h-the-taylor-series-expansion-for-fx-h-is-a-textfleft-textx-right-texthfleft-textx-right-fractexth22textf\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Engineering maths","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/engineering-maths\/"},{"@type":"ListItem","position":4,"name":"Calculus","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/engineering-maths\/calculus\/"},{"@type":"ListItem","position":5,"name":"For a small value of h, the Taylor series expansion for f(x + h) is A. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] B. \\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] C. \\[{\\text{f}}\\left( {\\text{x}} \\right) + {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{{2!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^3}}}{{3!}}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\] D. \\[{\\text{f}}\\left( {\\text{x}} \\right) – {\\text{hf}}’\\left( {\\text{x}} \\right) + \\frac{{{{\\text{h}}^2}}}{2}{\\text{f}}”\\left( {\\text{x}} \\right) – \\frac{{{{\\text{h}}^3}}}{3}{\\text{f}}”\\left( {\\text{x}} \\right) + \\,…\\,\\infty \\]"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required 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