Calculus 3- Show work.

14.4Differentiabilityandtangentplanes:

1.

Find an equation of the tangent plane at the given point. f (21,9) 2 % (4, 5) (Use symbolic notation and fractions where needed.) Find an equation of the tangent plane at the given point: F[r, 3) = (7-2305 + 23\") , [11 1) Z: Find an equation of the tangent plane to the graph of x, 3;) = 1121021.!-2 611,12) at point (1, 1]. (Use symbolic notation and fractions where needed.) z : help (fractions) Find the point on the graph of: = y"2 2:2 at which vector 11 = (20, 8, 1) is normal to the tangent plane. P : Use the linear approximation to it; y) = 1.! g: at (3, 4) to estimate %. g N _ 99 N help (fractions) The percentage error is % \fUse the linear approximation to x, y) = \"1:12\" 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} m help (fractions) The percentage error is % \fSuppose that the plane tangent to the surface z : x, '9) at (1, 4, 5} has equation 2 l 5: + 13; = 4. Estimate f(1.1, 4.1). (Use decimal notation. Give your answer to three decimal places.) f(1.1, 4.1) a 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 2AT +. Ah h AV x 100% o 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 6.9111 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 enor in V: %