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

2024
Views:

195

Pages:

2
Author:

Jalen W.

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 1. Find ∂f ∂x ∂f and for the following function. ∂y 3 2 f(x,y) = x − 6xy − 9y ∂f ∂x ∂f ∂y 2 = 3x − 6y = − 6x − 18y 2. Find ∂f ∂x ∂f and for the following function. ∂y 3 f(x,y) = x − 9 (6y + 5) ∂f ∂x ∂f ∂y 2 = 3x (6y + 5) = 6 x −9 3. Find 3 ∂f ∂x ∂x ∂f ∂y = ∂y . 2 f(x,y) = ∂f ∂f and 2 3x + 2y 3x 2 2 (Type an exactanswer, using radicals asneeded.) 3x + 2y = 2y 2 2 (Type an exactanswer, using radicals asneeded.) 3x + 2y 4. Find ∂f / ∂x and ∂f / ∂y. f(x,y) = e (x + y + 8) ∂f / ∂x = ex + y + 8 ∂f / ∂y = ex + y + 8 2 2 5. For the function f(x,y,z) = 1 + 3xy − 5z , find fx , fy , and fz . 2 fx = 3y fy = 6xy fz = − 10z Assignment: Section 14.3 Enhanced Assign 6. For the function f(x,y,z) = ln (6x + 7y + 2z), find fx , fy , and fz . 6 fx = 6x + 7y + 2z 7 fy = 6x + 7y + 2z fz = 6x + 7y + 2z 2 7. Find all thesecond-order partial derivatives of the function. r(x,y) = ln (x + 5y) ∂r 2 2 ∂x ∂r = (x + 5y) 2 ∂y∂x ∂r = − = − ∂y 5 = − 2 5 (x + 5y) 2 2 2 (x + 5y) 2 ∂x∂y ∂r 1 − 2 25 (x + 5y) 2

Section 14.3 Enhanced Assign

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