AP Calculus BC : 1.10 Exploring Types of 3 Discontinuities- Exam Style questions with Answer- MCQ

Question

The graph of a function f is shown in the figure above. At what value of x does f have a jump discontinuity?

A x=1

B x=3

C x=4

D x=5

Answer/Explanation

Ans:A

f

has a jump discontinuity at x=

1

 

Question

The function f has a removable discontinuity at x=

3

. Which of the following could be the graph of f?

A

B

Answer/Explanation

Ans:A

.This graph has a removable discontinuity at x=3, because \(\lim_{x\rightarrow 3^{-}}f(x)=\lim_{x\rightarrow 3^{+}}f(x)\) even though the function is not defined at x=3

Question

The function f

 is defined above. Which of the following statements is true?

A f is continuous at x=3.

B f

has a removable discontinuity at x=3

.

C f has a jump discontinuity at x=3.

D f

f

 has a discontinuity due to a vertical asymptote at x=3.

Answer/Explanation

Ans:B

\(\lim_{x\rightarrow 3}=\lim_{x\rightarrow 3}\frac{2x^{2}-5x-3}{x-3}=\lim_{x\rightarrow 3}\frac{(x-3)(2x+1)}{(x-3)}=\lim_{x\rightarrow 3}(2x+1)=2.3+1=7\)

\(\lim_{x\rightarrow 3}f(x)=7\) but \(f(3)\neq 7\)  so there is a removable discontinuity at x=3

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