University:
Georgia Southern University
Course:
MATH 2243 | Calculus 3
Academic year:

2024
Views:

323

Pages:

2
Author:

Jalen W.

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 Assignment: Sec 14.5 Enhanced Assign 1. Find the gradient of the function f(x,y) = 3y − 8x at the point (5,4). Then sketch the gradient and the level curve that passes through that point. ∇f (5,4) = ( −8 )i + ( 3 )j (Simplify youranswer.) Which of the following shows the level curve with the gradient at the point (5,4)? A. B. 20 C. y 20 10 y 20 10 10 x -20 -10 10 x 20 -20 -10 10 x 20 -20 -10 10 -10 -10 -10 -20 -20 -20 2. Find the gradient of the function f(x,y) = through the point. ∇f ( − 2,4) = y 4x + 3y at the point ( − 2,4). Then sketch the gradient together with the level curve that passes 3 i+ 1 20 j 4 (Type integers or simplifiedfractions.) Choose the correct graph below. A. B. C. y 5 5 y 5 x -5 y 5 x 1 -1 D. -5 -1 1 x -5 -1 1 x -5 3. Find ∇f at the given point. 3 3 2 f(x,y,z) = x + y − 3z + z ln x, ∇f (1,2,4) = 7 i + ( (1,2,4) 12 )j + ( − 24 4. Find the derivative of the function at P0 in the direction of A. 2 f(x,y) = 2xy − y , P0 ( − 6, − 4), A = 10i − 9j DA f ( − 6, − 4) = − 80 + 36 181 (Type an exactanswer, using radicals as needed.) y )k (Simplify youranswers.) -1 1 5. Find the derivative of the function at P0 in the direction of A. f(x,y,z) = xy + yz + zx, 12 DA f ( − 1,1,2) = 6. Find P0 ( − 1,1,2), 11 x − 10y − 1 lim (x,y)→(1,0) x − 10y − 1 A = 2i + 6j − 9k (Simplify youranswer.) by rewriting the fraction first. x − 10y ≠ 1 x − 10y − 1 lim (x,y)→(1,0) x − 10y − 1 = 1 2 x − 10y ≠ 1 (Simplify youranswer.) 7. Sketch the curve f(x,y) = c, together with ∇f and the tangent line at the given point. Then write an equation for the tangent line. 2 2 x + y = 5, 2, 3 Choose the correct sketch. A. B. y C. y x Choose the correct equation for the tangent line. A. 2 3 x − 2 2 y = − 10 B. 2 2 x + 2 3 y = 10 C. 2 2 x + 2 3 y = − 10 D. 2 3 x − 2 2 y = 10 D. y x y x x