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(AP) Let f be the function as defined. Which of the following statements is true? f(x) = /Ixl – 2 a. fis continuous but not differentiable at x = 2 b. fis differentiable at x = 2 c. fis not continuous at x = 2 d. x = 2 is a vertical asymptote of the graph of f lim f(x) # 0 е. X-2

(AP) Let f be the function as defined. Which of the following statements is true? f(x) = /Ixl – 2 a. fis continuous but not differentiable at x = 2 b. fis differentiable at x = 2 c. fis not continuous at x = 2 d. x = 2 is a vertical asymptote of the graph of f lim f(x) # 0 е. X-2

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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Which statement is true?

(AP) Let \( f \) be the function as defined. Which of the following statements is true? \[ f(x) = \sqrt{|x|} - 2 \] a. \( f \) is continuous but not differentiable at \( x = 2 \) b. \( f \) is differentiable at \( x = 2 \) c. \( f \) is not continuous at \( x = 2 \) d. \( x = 2 \) is a vertical asymptote of the graph of \( f \) e. \( \lim_{{x \to 2}} f(x) \neq 0 \)
Transcribed Image Text:(AP) Let \( f \) be the function as defined. Which of the following statements is true? \[ f(x) = \sqrt{|x|} - 2 \] a. \( f \) is continuous but not differentiable at \( x = 2 \) b. \( f \) is differentiable at \( x = 2 \) c. \( f \) is not continuous at \( x = 2 \) d. \( x = 2 \) is a vertical asymptote of the graph of \( f \) e. \( \lim_{{x \to 2}} f(x) \neq 0 \)
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