University:
Georgia Southern University
Course:
MATH 1441 | Calculus I
Academic year:

2024
Views:

166

Pages:

2
Author:

Jalen W.

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/12/24 1. Use implicit differentiation to find 2 dy dx . 2 2x y + 5xy = − 6 dy dx 2. 2 − 5y − 4xy = 2x(x + 5y) Use implicit differentiation to find 4 dy dx . 4 x + y = 24xy dy dx 3. 6y − x = 3 3 y − 6x Use implicit differentiation to find 5 dy dx . 5 x − 35xy + y = 1 dy dx 4. 4 = 4 y − 7x Use implicit differentiation to find 2 5y = dy dx 5. − x + 7y dy dx . 4x − 3 4x + 3 12 = 5y(4x + 3) 2 Use implicit differentiation to find dy dx . x = sec y dy dx 6. = 1 sec y tan y Use implicit differentiation to find x − tan(xy) = − 1 dy dx 2 = 1 − y sec (xy) 2 x sec (xy) dy dx . Assignment: Section 3.7 Enhanced Assignment 7. dy Find e dy 7x = dx . dx 8. = sin (x + 2y) 7e − cos (x + 2y) 2 cos (x + 2y) dr Find 7x for θ dθ 4 − 5 − +r 4 5 = − 3. 9 dr dθ = 5 r − 9 θ5 9. dy Use implicit differentiation to find 2 dx 2 and d y 2 . dx 2 4x + y = 1 dy = dx 4x − 2 y 2 d y 4y + 16x = − 2 3 dx 10. 2 y 2 3 3 If x + y = 72, find the value of d y 2 at the point (4,2). dx 2 d y The value of at the point (4,2) is 2 dx (Type a simplifiedfraction.) − 18 . 11. Find the slope of the curve at the given point. 3 6 2y + 9x = 5y + 6x at (1,1) 3 6 The slope of the curve 2y + 9x = 5y + 6x at(1,1) is (Type a simplifiedfraction.) − 48 . 12. The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at the given point. 2 2 x + xy − y = − 11, (2,5) (a) Give the equation of the line that is tangent to the curve at the given point. y= 9 8 x+ 11 4 (b) Give the equation of the line that is normal to the curve at the given point. y= − 8 9 x+ 61 9