{"id":20137,"date":"2024-04-15T05:48:53","date_gmt":"2024-04-15T05:48:53","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20137"},"modified":"2024-04-15T05:48:53","modified_gmt":"2024-04-15T05:48:53","slug":"if-a-function-is-continuous-at-a-point-a-the-limit-of-the-function-may-not-exist-at-the-point-b-the-function-must-be-derivable-at-the-point-c-the-limit-of-the-function-at-the-point-tends-to-infini","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-a-function-is-continuous-at-a-point-a-the-limit-of-the-function-may-not-exist-at-the-point-b-the-function-must-be-derivable-at-the-point-c-the-limit-of-the-function-at-the-point-tends-to-infini\/","title":{"rendered":"If a function is continuous at a point, A. the limit of the function may not exist at the point B. the function must be derivable at the point C. the limit of the function at the point tends to infinity D. the limit must exist at the point and the value of limit should be same as the value of the function at that point"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a990d83e7d2a\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    the limit of the function may not exist at the point                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    the function must be derivable at the point                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    the limit of the function at the point tends to infinity                <\/div>\r\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is: D. The limit must exist at the point and the value of limit should be same as the value of the function at that point.<\/p>\n<p>A function is continuous at a point if the following two conditions are met:<\/p>\n<ol>\n<li>The function has a defined value at the point.<\/li>\n<li>The limit of the function as $x$ approaches the point exists and is equal to the value of the function at the point.<\/li>\n<\/ol>\n<p>In other words, if a function is continuous at a point, then the graph of the function must pass through that point and the two-sided limit of the function as $x$ approaches the point must be equal to the value of the function at the point.<\/p>\n<p>Option A is incorrect because if a function is continuous at a point, then the limit of the function must exist at that point.<\/p>\n<p>Option B is incorrect because a function can be continuous at a point without being derivable at that point. For example, the function $f(x) = |x|$ is continuous at $x = 0$, but it is not derivable at $x = 0$.<\/p>\n<p>Option C is incorrect because the limit of a function at a point can be any finite <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> number, including infinity. For example, the function $f(x) = \\frac{1}{x}$ has a limit of infinity as $x$ approaches zero.<\/p>\n<p>I hope this explanation is helpful!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If a function is continuous at a point, A. the limit of the function may not exist at the point B. the function must be derivable at the point C. the limit of the function at the point tends to infinity D. the limit must exist at the point and the value of limit should be same as the value of the function at that point<\/title>\n<meta name=\"robots\" content=\"index, follow, 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