Quiz (Tangent Planes, Approximations, and Differentiability)

Show all work and justify each step.

(1) Find the tangent plane to the given surfaces at the given point.

    (i) Determine the standard-form equation for the tangent plane to the surface at .

    (ii) Determine the standard-form equation for the tangent plane to the surface at .

(2) Determine the total differential of the functions

.

(3) Use linear approximation (differentials) to find approximate values for

and      

(4) Show that the functions and are differentiable.

(5) Show that if and are sufficiently close to zero and is differentiable at then  

;

and use this approximation for the expressions and around

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Cite this as:
Tangent Planes Approximations And Differentiability Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/tangent-planes-approximations-and-differentiability-quiz.html