(a) Let f(x,y) = sqrt{x^2 + y^2.} Find an equation of the tangent plane of the graph z =...
Question:
(a) Let {eq}f(x,y) = \sqrt{x^2 + y^2.} {/eq} Find an equation of the tangent plane of the graph {eq}z = f(x,y) {/eq} at (3, 4, 5).
(b) Use a linear approximation to estimate {eq}f(3.1, 4.2). {/eq}
Linearization:
The equation of the tangent plane to a function of two variables {eq}f(x,y) {/eq} at point {eq}(x_0,y_0) {/eq}
is found by arresting the series of Taylor at the first order terms, i.e.
{eq}L(x,y) = f(x_0,y_0) + f_x(x_0,y_0) (x-x_0) + f_y(x_0,y_0) (y-y_0) {/eq}
where {eq}f_x, \; f_y {/eq} are the first partial derivatives of the function.
Answer and Explanation:
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View this answer(a) Consider the function
{eq}f(x,y) = \sqrt{x^2 + y^2.} {/eq}
The equation of the tangent plane at point at (3, 4, 5) is calculated as
{eq}f(3,4)...
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