[amp_mcq option1=”\\[\\sqrt {\\frac{{13}}{9}} \\]” option2=”\\[\\sqrt {\\frac{9}{2}} \\]” option3=”\\[\\sqrt 5 \\]” option4=”\\[\\frac{9}{2}\\]” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\sqrt {\\frac{{13}}{9}}}$.<\/p>\n
The gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and its magnitude is the magnitude of the greatest rate of increase.<\/p>\n
The gradient of the scalar field $\\text{u} = \\frac{{{{\\text{x}}^2}}}{2} + \\frac{{{{\\text{y}}^2}}}{3}$ is given by<\/p>\n
$$\\nabla \\text{u} = \\left( \\frac{\\partial \\text{u}}{\\partial x}, \\frac{\\partial \\text{u}}{\\partial y} \\right) = \\left( \\frac{x}{2}, \\frac{y}{3} \\right).$$<\/p>\n
The magnitude of the gradient at the point $(1, 3)$ is then given by<\/p>\n
$$\\left| \\nabla \\text{u} \\right| = \\sqrt{\\left( \\frac{1}{2} \\right)^2 + \\left( \\frac{3}{3} \\right)^2} = \\sqrt{\\frac{{13}}{9}}.$$<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”\\[\\sqrt {\\frac{{13}}{9}} \\]” option2=”\\[\\sqrt {\\frac{9}{2}} \\]” option3=”\\[\\sqrt 5 \\]” option4=”\\[\\frac{9}{2}\\]” correct=”option1″]<\/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-20184","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\n