solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks.

1. [-/1 Points] DETAILS SCALCET9 14.4.001. The graph of a function fis shown below. Graph Graph Description a Interactive 3D Graph @ Help 2 20 10 Find an equation of the tangent plane to the surface z = f(x, y) at the specified point. f(x, y) = 17 - x2 - y2 Need Help? Read It2. [-/1 Points] DETAILS SCALCET9 14.4.003.EP. Consider the following surface. z = 2x2 + 12 - 5y Let z = f(x, y). Find f (x, y) and f (x, y). fx (x, y ) = f(x, v) = Find an equation of the tangent plane to the given surface at the point (1, 2, -4). Need Help? Read It 3. [-/1 Points] DETAILS SCALCET9 14.4.007. Find an equation of the tangent plane to the given surface at the specified point. Z = 7Vy (-1, 1, -7) X Need Help? Read It4. [-/1 Points] DETAILS SCALCET9 14.4.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the tangent plane to the given surface at the specified point. z = x sin(y - x), (5, 5, 0) Need Help? Read It Watch It 5. [-/1 Points] DETAILS SCALCET9 14.4.016. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Explain why the function is differentiable at the given point. f( x, v ) = y tan(x), (#. 4) The partial derivatives are fx(x, y) = and f (x, y ) = 50 1, ( # , 4 ) = [and f ( # , 4 ) - . Using n as an arbitrary integer, both fy and fy are continuous functions for x # so f is differentiable at (#, 4) Find the linearization L(x, y) of the function at ( #, 4) L ( X, y ) = Need Help? Read It6. [-/1 Points] DETAILS SCALCET9 14.4.027.EP. Consider the following function. f( x, y, z ) = V x2 + 2+ zz Find f (x, y, z), f (x, y, z), and f= (x, y, z). Fx ( x, V, z) = f ( x, y, z) = f= ( x, V, Z ) = Find the linear approximation of the function f(x, y, z) = v x2 + y2 + 22 at (9, 2, 6). f ( x , V, Z ) A Use the linear approximation to approximate the number v 9.032 + 1.992 + 5.982. (Round your answer to four decimal places.) A(9.03, 1.99, 5.98) 2 Need Help? Read It 7. [-/1 Points] DETAILS SCALCET9 14.4.032. Find the differential of the function. z = x In(y> + 7) dz = Jax + dy Need Help? Read It8. [-/1 Points] DETAILS SCALCET9 14.4.033. MY NOTES ASK YOUR TEAC Find the differential of the function. z = e-* cos(9nt) dz = dx + dt Need Help? Read It Watch It 9. [-/1 Points] DETAILS SCALCET9 14.4.039. MY NOTES ASK YOUR TEA If z = 3x2 + y2 and (x, y) changes from (1, 3) to (0.95, 3.1), compare the values of Az and dz. dz = Az = Need Help? Read It Watch It 10. [-/1 Points] DETAILS SCALCET9 14.4.041.MI. MY NOTES ASK YOUR TEAC The length and width of a rectangle are measured as 42 cm and 46 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle. cm Need Help? Read It Watch It Master It