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

2024
Views:

137

Pages:

2
Author:

Jalen W.

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 1. Describe the given region in polar coordinates. 10 Assignment: Sect 15.4 Enhanced Assign y x -10 10 -10 3π ≤θ≤ 2 2π , 0 ≤r≤ 6 (Type an exactanswer, using π asneeded.) 2. Describe the given region in polar coordinates. 7 y 5 x 5 π region is π ≤θ≤ 6 π ≤θ≤ 0 The lower portion of the region is 5 , 2 , 6 ≤r≤ 7 3 5 7 csc θ ≤r≤ 7 3 sec θ . The upper portion of the . (Type an exactanswer, using π asneeded.) 3. Find ∇f at the given point. 2 2 2 f(x,y,z) = x + y − 4z + z ln x, ∇f (1,4,3) = 5 i + ( 4. 8 13 Change the Cartesian integral (1,4,3) ∫ − 13 ∫ 0 )j + ( − 24 )k (Simplify youranswers.) 169 − x2 dy dx into an equivalent polar integral. Then evaluate the polar integral. Change the Cartesian integral into an equivalent polar integral. 13 ∫ − 13 ∫ 0 169 − x2 ∫ π dy dx = 0 (Type exactanswers, using π asneeded.) The value of the double integral is ∫0 169 2 (Type an exactanswer, using π asneeded.) π 13 r . dr dθ 5. Sketch the region of integration and convert the polar sum of integrals to a Cartesian integral or sum of integrals. Do not evaluate the integrals. tan −1 ∫ (7 / 3) 3 sec θ ∫ 0 0 π/ 2 7 csc θ ∫ 7 r dr dθ + tan −1 ∫ 7 r dr dθ 0 (7 / 3) Sketch the region of integration. Choose the correct graph below. A. B. 2 y C. y 10 D. 2 y 7 x -2 y x x 2 -7 -2 -2 7 -4 x 2 -7 -2 7 -7 Convert the polar integral to a Cartesian integral or sum of integrals. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exactanswers.) A. The Cartesian integral can be written as a single integral. 7 3 ∫ 0 ∫ 2 2 3 x +y dx dy 0 B. The Cartesian integral cannot be written as a single integral. ∫ 0 ∫ 0 dx dy + ∫ 0 ∫ 0 dx dy