AP Calculus BC : 1.8 Determining Limits Using the Squeeze Theorem- Exam Style questions with Answer- MCQ

Question

Let

f

be a function of 

x

. The value of can be found using the squeeze theorem with the functions g

g

 and h

h

. Which of the following could be graphs of f,

g

, and h ?

A

B

C

D

Answer/Explanation

Ans:D

 The hypothesis conditions of the squeeze theorem are satisfied, since g(x)f(x)h(x)

)

on the interval shown and \(\lim_{x\rightarrow a}g(x)=\lim_{x\rightarrow a}h(x) \) .Therefore, \(\lim_{x\rightarrow a}f(x)\)can be found using the squeeze theorem with these functions g and 

h

 

Question

The function g is given by \(g(x)=\frac{1}{x^{2}-4x+5}\).The function h

h

is given by \(h(x)=\frac{2x^{2}-8x+10}{x^{2}-4x+6}\). If f is a function that satisfies g(x)f(x)h(x) for

0<x<5

, what is ?

A  0

B 1

C  2

D The limit cannot be determined from the information given.

Answer/Explanation

Ans: B

Since  and it can be concluded from the squeeze theorem that because g(x)f(x)h(x) for 0<x<5

Question

The function f is defined for all x in the interval 3<x<6. Which of the following statements, if true, implies that ?

A There exists a function g with f(x)≤g(x) for 3<x<6, and

B There exists a function g with g(x)≤f(x) for 3<x<6, and

C There exist functions g and h with g(x)≤f(x)≤h(x) for 3<x<6, and   and

D There exist functions g and hh with g(x)≤f(x)≤h(x) for 3<x<6, and

Answer/Explanation

Ans: D

The hypothesis conditions of the squeeze theorem are confirmed, so it may be concluded that

Question 

 Find the limit:\(\lim_{x\rightarrow -\infty }\frac{\sin \Theta }{\Theta }\)
(A) 0
(B) −1
(C) −∞
(D) The limit does not exist.

Answer/Explanation

Ans:(A)

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