Sec. 14.1 Enhanced Assign | Georgia Southern University

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

2024
Views:

139

Pages:

3
Author:

Jalen W.

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 Assignment: Sec. 14.1 Enhanced Assign 2 2 1. Let f(x,y) = x − 2xy − y . Compute f(7,0) and f(7, − 4). f(7,0) = 49 f(7, − 4) = (Simplify youranswer.) 89 (Simplify youranswer.) 2. Find the specific function values. Complete parts (a) through (d) below. x−y f (x,y,z) = 2 y +z 2 9 (a) f (5, − 4,3) = 1 1 (b) f 1, , − 2 6 (c) f 0, − 1 6 (Simplify youranswer.) 25 9 = (Simplify youranswer.) 5 ,0 = (Simplify youranswer.) 6 (d) f (4,4,300) = 0 (Simplify youranswer.) 3. Find and sketch the domain of the function. f(x,y) = y−x−2 Find the domain of the function. Express the domain so that coefficients have no common factors other than 1. Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice. A. The domain is all points(x,y) satisfying =0 B. The domain is all points(x,y) satisfying y−x−2 ≥0 C. The domain is all points(x,y) satisfying ≠0 D. The domain is all points(x,y) satisfying >0 E. All points in thexy-plane. Choose the correct sketch below. The domain is shaded in yellow. A. B. 10 y C. 10 x -10 10 -10 y D. 10 x -10 10 -10 y 10 x -10 10 -10 y x -10 10 -10 4. Find and sketch the domain for the function. 2 2 f(x,y) = ln x + y − 36 Find the domain for the function. Express the domain so that coefficients have no common factors other than 1. Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice. A. The domain is all points(x,y) satisfying ≠ 0. 2 B. The domain is all points(x,y) satisfying 2 > 0. x + y − 36 C. The domain is all points(x,y) satisfying = 0. D. The domain is all points(x,y) satisfying ≥ 0. E. The domain is the entire plane(x,y). Choose the correct sketch below. The domain is shaded in yellow. A. B. C. y 10 10 10 y 10 x -10 D. y 10 x -10 -10 10 y x -10 -10 x 10 -10 -10 10 -10 5. Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values of c. Refer to these level curves as a contour map. z = 3x − 2y; c = − 2, − 1, 0, 1, 2 Choose the correct graph below. A. B. z=2 3 y C. 2 2 z=2 -2 2 z= −2 y -2 2 z= −2 -2 2 z= −2 z= −2 x x x -2 D. y -2 y x 2 -2 2 z=2 -3 -2 z=2 6. Use the graph to determine the domain and range of the function. 1 y What is thedomain? [ − 2π,2π] ( Type an integer or a fraction. Simplify your answer. Type your answer in interval notation.) What is therange? [ − 1,1] ( Type an integer or a fraction. Simplify your answer. Type your answer in interval notation.) 2π -10 − 2π x 10 -1 7. Sketch a typical level surface for the function f(x,y,z) = x2 + z2 . Choose the correct graph of a level surface below. A. B. C. D. 8. Sketch a typical level surface for the function f(x,y,z) = 6z − 6x2 − 6y2 . Choose the correct answer below. A. B. 2 9. Find and simplify the expression if f(x) = x − 11. f(2x) f(2x) = 2 4x − 11 (Simplify youranswer.) C.