Questions 1-5: NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS 1. Determine lim tan(x)-1 X- 4 Use the table and graph to answer Questions 2 - 4. Let f be the function whose graph, consisting of two line segments and one semicircle, is shown in the figure. Let g be a differentiable function. The table gives some values of g and its derivative g' at selected values of x. Let h be the function 1 defined by h(x) 4x² + In 6 2 0 -1 -2 f(x) y X g(x) g'(x) -2 3 5 0 4 0 1 1 3 4 -2 2 5 0 1 2. Part A: Is there a value of x, for 0 < x < 6, such that lim b-0 f(x+ h) − f(x) h - 0? Give a reason for your answer. Part B: Find the average rate of change of g over the interval [-2, 4]. 3. Part A: Let j be the function defined by j(x) = f(x) + 2g(x) - x3. Find j'(1). Show the work that leads to your answer. Part B: Let k be the function defined by k(x) = g(x)h(x). Find k '(1). Show the work that leads to your answer. g(x) Part C: Let m be the function defined by m(x)= Find m'(-2). Show the f(x) work that leads to your answer. 4. Determine the equation of the normal line to h(x) at x = 1. 5. If f() cos csc - cot, find f'(#).
Questions 1-5: NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS 1. Determine lim tan(x)-1 X- 4 Use the table and graph to answer Questions 2 - 4. Let f be the function whose graph, consisting of two line segments and one semicircle, is shown in the figure. Let g be a differentiable function. The table gives some values of g and its derivative g' at selected values of x. Let h be the function 1 defined by h(x) 4x² + In 6 2 0 -1 -2 f(x) y X g(x) g'(x) -2 3 5 0 4 0 1 1 3 4 -2 2 5 0 1 2. Part A: Is there a value of x, for 0 < x < 6, such that lim b-0 f(x+ h) − f(x) h - 0? Give a reason for your answer. Part B: Find the average rate of change of g over the interval [-2, 4]. 3. Part A: Let j be the function defined by j(x) = f(x) + 2g(x) - x3. Find j'(1). Show the work that leads to your answer. Part B: Let k be the function defined by k(x) = g(x)h(x). Find k '(1). Show the work that leads to your answer. g(x) Part C: Let m be the function defined by m(x)= Find m'(-2). Show the f(x) work that leads to your answer. 4. Determine the equation of the normal line to h(x) at x = 1. 5. If f() cos csc - cot, find f'(#).
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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![Questions 1-5: NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS
1. Determine lim
tan(x)-1
X-
4
Use the table and graph to answer Questions 2 - 4.
Let f be the function whose graph, consisting of two line segments and one
semicircle, is shown in the figure. Let g be a differentiable function. The table gives
some values of g and its derivative g' at selected values of x. Let h be the function
1
defined by h(x) 4x² + In
6
2
0
-1
-2
f(x)
y
X
g(x)
g'(x)
-2
3
5
0
4
0
1
1
3
4
-2
2
5
0
1
2. Part A: Is there a value of x, for 0 < x < 6, such that lim
b-0
f(x+ h) − f(x)
h
-
0? Give
a reason for your answer.
Part B: Find the average rate of change of g over the interval [-2, 4].
3. Part A: Let j be the function defined by j(x) = f(x) + 2g(x) - x3. Find j'(1). Show
the work that leads to your answer.
Part B: Let k be the function defined by k(x) = g(x)h(x). Find k '(1). Show the
work that leads to your answer.
g(x)
Part C: Let m be the function defined by m(x)=
Find m'(-2). Show the
f(x)
work that leads to your answer.
4. Determine the equation of the normal line to h(x) at x = 1.
5. If f() cos csc - cot, find f'(#).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49c414ec-3770-4bc3-a638-b4fc7341686a%2F01ca921d-2f08-4bdf-a2ed-e1422b3e23e5%2Fi36dfup_processed.png&w=3840&q=75)
Transcribed Image Text:Questions 1-5: NO CALCULATOR IS ALLOWED FOR THESE QUESTIONS
1. Determine lim
tan(x)-1
X-
4
Use the table and graph to answer Questions 2 - 4.
Let f be the function whose graph, consisting of two line segments and one
semicircle, is shown in the figure. Let g be a differentiable function. The table gives
some values of g and its derivative g' at selected values of x. Let h be the function
1
defined by h(x) 4x² + In
6
2
0
-1
-2
f(x)
y
X
g(x)
g'(x)
-2
3
5
0
4
0
1
1
3
4
-2
2
5
0
1
2. Part A: Is there a value of x, for 0 < x < 6, such that lim
b-0
f(x+ h) − f(x)
h
-
0? Give
a reason for your answer.
Part B: Find the average rate of change of g over the interval [-2, 4].
3. Part A: Let j be the function defined by j(x) = f(x) + 2g(x) - x3. Find j'(1). Show
the work that leads to your answer.
Part B: Let k be the function defined by k(x) = g(x)h(x). Find k '(1). Show the
work that leads to your answer.
g(x)
Part C: Let m be the function defined by m(x)=
Find m'(-2). Show the
f(x)
work that leads to your answer.
4. Determine the equation of the normal line to h(x) at x = 1.
5. If f() cos csc - cot, find f'(#).
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