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Question 12 Suppose that k is a real constant such that all the tangents to the curve y = In(x2 + 1) + kx have negative slopes. Which of the following must always be true? (a) k <-2 (b) k < -1 (c) k >1 (d) k| < 1 (e) none of these Question 13 sin(Vr – 1) lim x - 1 (a) 1 (b) 1/2 (c) 2 (d) oo (e) none of these Question 14 Suppose that f'(x) > 0 for all x E R. Let g(x) = f(2x – x2) for all x E R. Then on [3, 5], (a) g(3) is the min and g(5) is the max value (b) g(3) is the max and g(5) is the min value (c) g(xo) is the max value of g for some 3 < xo < 5 (d) g(uo) is the min value of g for some 3 < uo < 5 (e) none of these Question 15 If f'(0) = 1, then f(sin 3x) – f(0) lim (a) 3 (b) 1 (c) 1/3 (d) 0 (e) none of these

Question 12 Suppose that k is a real constant such that all the tangents to the curve y = In(x2 + 1) + kx have negative slopes. Which of the following must always be true? (a) k <-2 (b) k < -1 (c) k >1 (d) k| < 1 (e) none of these Question 13 sin(Vr – 1) lim x - 1 (a) 1 (b) 1/2 (c) 2 (d) oo (e) none of these Question 14 Suppose that f'(x) > 0 for all x E R. Let g(x) = f(2x – x2) for all x E R. Then on [3, 5], (a) g(3) is the min and g(5) is the max value (b) g(3) is the max and g(5) is the min value (c) g(xo) is the max value of g for some 3 < xo < 5 (d) g(uo) is the min value of g for some 3 < uo < 5 (e) none of these Question 15 If f'(0) = 1, then f(sin 3x) – f(0) lim (a) 3 (b) 1 (c) 1/3 (d) 0 (e) none of these

Calculus: Early Transcendentals
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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Question 12 Suppose that k is a real constant such that all the tangents to the curve y = In(x² + 1) + kx have negative slopes. Which of the following must always be true? (a) k < -2 (b) k < –1 (c) k > 1 (d) |k| < 1 (e) none of these Question 13 sin(Va – 1) lim x→1 x – 1 (a) 1 (b) 1/2 (c) 2 (d) ∞ (e) none of these Question 14 Suppose that f'(x) > 0 for all x E R. Let g(x)= f(2x – x²) for all x E R. Then on [3, 5], (a) g(3) is the min and g(5) is the max value (b) g(3) is the max and g(5) is the min value (c) g(xo) is the max value of g for some 3 < xo < 5 (d) g(uo) is the min value of g for some 3 < uo < 5 (e) none of these Question 15 If f'(0) = 1, then f(sin 3x) – f(0) lim x→0 (а) 3 (b) 1 (c) 1/3 (d) 0 (e) none of these
Transcribed Image Text:Question 12 Suppose that k is a real constant such that all the tangents to the curve y = In(x² + 1) + kx have negative slopes. Which of the following must always be true? (a) k < -2 (b) k < –1 (c) k > 1 (d) |k| < 1 (e) none of these Question 13 sin(Va – 1) lim x→1 x – 1 (a) 1 (b) 1/2 (c) 2 (d) ∞ (e) none of these Question 14 Suppose that f'(x) > 0 for all x E R. Let g(x)= f(2x – x²) for all x E R. Then on [3, 5], (a) g(3) is the min and g(5) is the max value (b) g(3) is the max and g(5) is the min value (c) g(xo) is the max value of g for some 3 < xo < 5 (d) g(uo) is the min value of g for some 3 < uo < 5 (e) none of these Question 15 If f'(0) = 1, then f(sin 3x) – f(0) lim x→0 (а) 3 (b) 1 (c) 1/3 (d) 0 (e) none of these
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