Question
Let
be a function of
. The value of 
can be found using the squeeze theorem with the functions g
and h
. Which of the following could be graphs of f,
, 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
Question
The function g is given by \(g(x)=\frac{1}{x^{2}-4x+5}\).The function 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
, 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)