11) If f is a continuous function such that f(2)= 6, which of the following must be true? f(x)-f(2)_ x-2 A) lim 4) x = 0 2=6 B) lim f(2x) = 12 C) lim[f(x)]= x-1 12) The function f(x)=- x-1 x²-3x+2 x = 5 only B) x = 1 13) The function g as defined by g(x)= B) x = 0 only 4) What is the value of lim - *→ x-1 -has vertical asymptotes at which values? B)-1/2 C) x = 2 |x-5|(x+5) x(x²-25) = 36 D) lim f(x²)=36 x 2 cont C) 00 C) x = 0 and x = 5 only D) x = 1 and x = 2 has vertical asymptotes at D) x = -5, x= 0 and x = 5 only D) -00
11) If f is a continuous function such that f(2)= 6, which of the following must be true? f(x)-f(2)_ x-2 A) lim 4) x = 0 2=6 B) lim f(2x) = 12 C) lim[f(x)]= x-1 12) The function f(x)=- x-1 x²-3x+2 x = 5 only B) x = 1 13) The function g as defined by g(x)= B) x = 0 only 4) What is the value of lim - *→ x-1 -has vertical asymptotes at which values? B)-1/2 C) x = 2 |x-5|(x+5) x(x²-25) = 36 D) lim f(x²)=36 x 2 cont C) 00 C) x = 0 and x = 5 only D) x = 1 and x = 2 has vertical asymptotes at D) x = -5, x= 0 and x = 5 only D) -00
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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![**Math Problems and Solutions**
**11) If \( f \) is a continuous function such that \( f(2) = 6 \), which of the following must be true?**
A) \( \lim_{x \to 1} \frac{f(x) - f(2)}{x - 2} = 6 \)
B) \( \lim_{x \to 1} f(2x) = 12 \)
C) \( \lim_{x \to 2} [f(x)]^2 = 36 \)
D) \( \lim_{x \to 2} f(x^2) = 36 \)
**12) The function \( f(x) = \frac{x - 1}{x^2 - 3x + 2} \) has vertical asymptotes at which values?**
A) \( x = 0 \)
B) \( x = 1 \)
C) \( x = 2 \)
D) \( x = 1 \) and \( x = 2 \)
**13) The function \( g \) as defined by \( g(x) = \frac{x - 5}{x(x^2 - 25)} \) has vertical asymptotes at**
A) \( x = 5 \) only
B) \( x = 0 \) only
C) \( x = 0 \) and \( x = 5 \) only
D) \( x = -5, x = 0 \) and \( x = 5 \) only
**14) What is the value of \( \lim_{x \to 1} \frac{x^2}{x - 1} \)?**
A) 1
B) -1/2
C) \( \infty \)
D) -\( \infty \)
**15) Suppose the graph of \( y = f(x) \) has a vertical asymptote at \( x = 1 \). Which of the following could be true?**
I. \( f(1) = 2 \)
II. \( \lim_{x \to 1} f(x) = 2 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10b1f275-2c41-4985-b23a-aa3382c0d493%2F454710af-e836-4ccf-a080-b6ebbaa51cf3%2Fzji8znf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Math Problems and Solutions**
**11) If \( f \) is a continuous function such that \( f(2) = 6 \), which of the following must be true?**
A) \( \lim_{x \to 1} \frac{f(x) - f(2)}{x - 2} = 6 \)
B) \( \lim_{x \to 1} f(2x) = 12 \)
C) \( \lim_{x \to 2} [f(x)]^2 = 36 \)
D) \( \lim_{x \to 2} f(x^2) = 36 \)
**12) The function \( f(x) = \frac{x - 1}{x^2 - 3x + 2} \) has vertical asymptotes at which values?**
A) \( x = 0 \)
B) \( x = 1 \)
C) \( x = 2 \)
D) \( x = 1 \) and \( x = 2 \)
**13) The function \( g \) as defined by \( g(x) = \frac{x - 5}{x(x^2 - 25)} \) has vertical asymptotes at**
A) \( x = 5 \) only
B) \( x = 0 \) only
C) \( x = 0 \) and \( x = 5 \) only
D) \( x = -5, x = 0 \) and \( x = 5 \) only
**14) What is the value of \( \lim_{x \to 1} \frac{x^2}{x - 1} \)?**
A) 1
B) -1/2
C) \( \infty \)
D) -\( \infty \)
**15) Suppose the graph of \( y = f(x) \) has a vertical asymptote at \( x = 1 \). Which of the following could be true?**
I. \( f(1) = 2 \)
II. \( \lim_{x \to 1} f(x) = 2 \)
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