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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'(#).

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'(#).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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'(#).
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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