Calculus 3: Show work please!

14.4 Differentiability and tangent planes.

1.

T Find an equation of the tangent plane at the given point. x, '9) = 7:, (4, 5) (Use symbolic notation and fractions where needed.) Find an equation of the tangent plane at the given point: F(r, s) = - (728 0.5 + 28-4) , (1, 1) =Find an equation of the tangent plane to the graph of its, 9) = 1110232 5'92) at point (1, 1]. (Use symbolic notation and fractions where needed.) 2 2 help (fractions) Find the point on the graph of; : y"z 2:2 at which vector 11 = (20, 81 1) is normal to the tangent plane. P = Use the linear approximation to x, 3;) = 3: at [3, 4) to estimate 13%. 8.1 N _ E N help (fractions) The percentage error is % Use the linear approximation of f(x, y) = ezz ty at (0, 0) to estimate f(0.02, 0.01)Use the linear approximation to x, y] = 311:!\" at [12, 5] to estimate f(12.1, 4.8). (Use decimal notation. Give your answer to four decimal places.) f(12.1, 4.8) 3 help (fractions) The percentage error is % \fSuppose that the plane tangent to the surface 2 : x, 3;) at (11 4, 5) has equation 2 + 5: + 13; = 4. Estimate f(1.1, 4.1). (Use decimal notation. Give your answer to three decimal places.) f[1.1, 4.1) m help (fractions) The volume of a cylinder of radius r and height h is V = mr-h. Calculate the percentage increase in V if r is increased by 2.3% and h is increased by 4.8%. Hint: Use the linear approximation to show that AV 2AT + Ah V h AV x 100% = The volume of a certain cylinder V is determined by measuring r and h. Which will lead to a greater error in V: O A. a 1% error in h O B. a 1% error in r is equivalent to a 1% error in h O C. a 1% error in rThe volume V of a cylinder is computed using the values 6.9m for the diameter and 7.4111 for the height. Use the linear approximation to estimate the maximum error in V if each of these values has a possible error of at most 10%. Percentage error in V: %