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1. f is continuous for a ≤ x ≤ b but not differentiable for some c such that a < c < b. Which of the following could be true? (A) x = c is a vertical asymptote of the graph of f. (D) f(c) is undefined. (B) lim f(x) + f(c) x-c (C) The graph of f has a cusp at x = c. (E) None of the above

1. f is continuous for a ≤ x ≤ b but not differentiable for some c such that a < c < b. Which of the following could be true? (A) x = c is a vertical asymptote of the graph of f. (D) f(c) is undefined. (B) lim f(x) + f(c) x-c (C) The graph of f has a cusp at x = c. (E) None of the above

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. f is continuous for a ≤ x ≤ b but not differentiable for some c such that a < c < b. Which of the following could be true? (A) x = c is a vertical asymptote of the graph of f. (D) f(c) is undefined. (A) 0 only (D) -2,2, and 6 only -2 -1 For which values of x does f'(x) = 0? (A) None (B) lim f(x) + f(c) x-c' m 1 2 3 4 (B) One (E) None of the above (B) 2 only (E) -2,0, 2, 4, and 6 (C) Two (C) The graph of f has a cusp at x = c. 5 f(x) If f'(x) = tan-¹(x²-x), at how many points is the tangent line to the graph of y = f(x) parallel to the line y 2x? (D) Three 6 7 (C) 0 and 4 only (E) Infinitely many
Transcribed Image Text:1. f is continuous for a ≤ x ≤ b but not differentiable for some c such that a < c < b. Which of the following could be true? (A) x = c is a vertical asymptote of the graph of f. (D) f(c) is undefined. (A) 0 only (D) -2,2, and 6 only -2 -1 For which values of x does f'(x) = 0? (A) None (B) lim f(x) + f(c) x-c' m 1 2 3 4 (B) One (E) None of the above (B) 2 only (E) -2,0, 2, 4, and 6 (C) Two (C) The graph of f has a cusp at x = c. 5 f(x) If f'(x) = tan-¹(x²-x), at how many points is the tangent line to the graph of y = f(x) parallel to the line y 2x? (D) Three 6 7 (C) 0 and 4 only (E) Infinitely many
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