Direction: Show all work for the following questions. If applicable, round to the nearest hundredth and circle all final answers. (10 pts) Use the limit definition of a derivative to find the slope of the tangent line of the function f(x) x2- 1. x 2 at x 3. Find f'(x) for the following functions using the shortcuts we have learned thus far. 2. f(x)=e-x. а. b. f(x) 2x + f(x)=2-9x C. X Evaluate each limit. If applicable, state why the limit doesn't exist. 3. x2+5x+10 lim а. 1 x-1 t2-9t+14 b. lim t--2 (t-2) 3x2 lim С. x-2 (x+2)(x-3) Зx2 4. Answer the following parts for the function f (x) (x+2)(x-3) Find the holes for f(x): a. Find any vertical asymptotes for f (x) (if any): b. Find any horizontal asymptotes (if any): С. Find the end behavior for f(x): d. n
Direction: Show all work for the following questions. If applicable, round to the nearest hundredth and circle all final answers. (10 pts) Use the limit definition of a derivative to find the slope of the tangent line of the function f(x) x2- 1. x 2 at x 3. Find f'(x) for the following functions using the shortcuts we have learned thus far. 2. f(x)=e-x. а. b. f(x) 2x + f(x)=2-9x C. X Evaluate each limit. If applicable, state why the limit doesn't exist. 3. x2+5x+10 lim а. 1 x-1 t2-9t+14 b. lim t--2 (t-2) 3x2 lim С. x-2 (x+2)(x-3) Зx2 4. Answer the following parts for the function f (x) (x+2)(x-3) Find the holes for f(x): a. Find any vertical asymptotes for f (x) (if any): b. Find any horizontal asymptotes (if any): С. Find the end behavior for f(x): d. n
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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please answer all the parts of question 2
Transcribed Image Text:Direction: Show all work for the following questions. If applicable, round to the nearest hundredth and circle all final
answers.
(10 pts) Use the limit definition of a derivative to find the slope of the tangent line of the function
f(x) x2-
1.
x 2 at x
3.
Find f'(x) for the following functions using the shortcuts we have learned thus far.
2.
f(x)=e-x.
а.
b. f(x) 2x +
f(x)=2-9x
C.
X
Evaluate each limit. If applicable, state why the limit doesn't exist.
3.
x2+5x+10
lim
а.
1
x-1
t2-9t+14
b. lim
t--2
(t-2)
3x2
lim
С.
x-2 (x+2)(x-3)
Зx2
4. Answer the following parts for the function f (x) (x+2)(x-3)
Find the holes for f(x):
a.
Find any vertical asymptotes for f (x) (if any):
b.
Find any horizontal asymptotes (if any):
С.
Find the end behavior for f(x):
d.
n
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