Workshop #26 | Answer Key

University:
University of North Dakota
Course:
Math 165 | Calculus I
Academic year:

2024
Views:

270

Pages:

1
Author:

Keenan Mcguire

Workshop #26 1. Compute the following limits: x sin x x→0 1 − cos x 2 x (b) lim 1 + x→∞ x (a) lim 1 (c) lim xe x x→0+ 1 1 − (d) lim 1 − cos x x→0+ x 2. (a) Find a function f (x) such that f 0 (x) = x2 − 5. (b) Find a function f (x) such that f 0 (x) = x2 − 5 and f (3) = 2. (c) How many functions are there such that f 0 (x) = x2 − 5? 3. If f 00 (x) = 1 x2 + 4x2 and f 0 (1) = 1 and f (1) = 5, then find f (x). 4. The girth of a shipping carton is the perimeter of an end. Shipping restrictions require that the sum of the girth and length not exceed 100 in. Find a rule that describes the volume of a package with a square end (the sum of whose girth and length equals 100 in) as a function of the width of an end. Then use calculus to find the maximum volume, and the dimensions that give that volume. 5. Differentiate the following. x2 + 3 tan x (b) g(x) = cos (ln(cos x)) (a) f (x) = 2x ) (c) h(x) = e(xe