UNIT 1 PROGRESS CHECK: MCQ
PART B CORRECT 100%
If f is the function defined by f(x)=x−11−1x, then limx→1f(x) is equivalent to which of the
following?
A
limx→1xlimx→1x
B
limx→12xlimx→12x
C
limx→1(x−11−x)limx→1(x−11−x)
D
limx→1(x−1)limx→1(1−1x) - ANSWERAnswer A
Correct. f(x)=x−11−1x=x−1xx−1x=x−1(x−1)x=xf(x)=x−11−1x=x−1xx−1x=x−1(x−1)x=x for
xx close to, but not equal to, 1. Therefore, limx→1f(x)=limx→1xlimx→1f(x)=limx→1x.
The function f is defined for all x in the interval 3<x<6. Which of the following
statements, if true, implies that limx→5f(x)=12?
A
There exists a function gg with f(x)≤g(x)f(x)≤g(x) for 3<x<63<x<6, and
limx→5g(x)=12limx→5g(x)=12.
B
There exists a function gg with g(x)≤f(x)g(x)≤f(x) for 3<x<63<x<6, and
limx→5g(x)=12limx→5g(x)=12.
C
There exist functions gg and hh with g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 3<x<63<x<6, and
limx→5g(x)=11limx→5g(x)=11 and limx→5h(x)=13limx→5h(x)=13.
D
There exist functions gg and hh with g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 3<x<63<x<6, and
limx→5g(x)=limx→5h(x)=12limx→5g(x)=limx→5h(x)=12. - ANSWERAnswer D
Correct. The hypothesis conditions of the squeeze theorem are confirmed, so it may be
concluded that limx→5f(x)=12limx→5f(x)=12.
Let f and g be functions such that limx→4g(x)=7 and limx→4f(x)g(x)=π. What is
limx→4f(x)?
A
π7π7
B
7+π7+π
C
7π7π
D
The limit cannot be determined from the information given. - ANSWERAnswer C
PART B CORRECT 100%
If f is the function defined by f(x)=x−11−1x, then limx→1f(x) is equivalent to which of the
following?
A
limx→1xlimx→1x
B
limx→12xlimx→12x
C
limx→1(x−11−x)limx→1(x−11−x)
D
limx→1(x−1)limx→1(1−1x) - ANSWERAnswer A
Correct. f(x)=x−11−1x=x−1xx−1x=x−1(x−1)x=xf(x)=x−11−1x=x−1xx−1x=x−1(x−1)x=x for
xx close to, but not equal to, 1. Therefore, limx→1f(x)=limx→1xlimx→1f(x)=limx→1x.
The function f is defined for all x in the interval 3<x<6. Which of the following
statements, if true, implies that limx→5f(x)=12?
A
There exists a function gg with f(x)≤g(x)f(x)≤g(x) for 3<x<63<x<6, and
limx→5g(x)=12limx→5g(x)=12.
B
There exists a function gg with g(x)≤f(x)g(x)≤f(x) for 3<x<63<x<6, and
limx→5g(x)=12limx→5g(x)=12.
C
There exist functions gg and hh with g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 3<x<63<x<6, and
limx→5g(x)=11limx→5g(x)=11 and limx→5h(x)=13limx→5h(x)=13.
D
There exist functions gg and hh with g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 3<x<63<x<6, and
limx→5g(x)=limx→5h(x)=12limx→5g(x)=limx→5h(x)=12. - ANSWERAnswer D
Correct. The hypothesis conditions of the squeeze theorem are confirmed, so it may be
concluded that limx→5f(x)=12limx→5f(x)=12.
Let f and g be functions such that limx→4g(x)=7 and limx→4f(x)g(x)=π. What is
limx→4f(x)?
A
π7π7
B
7+π7+π
C
7π7π
D
The limit cannot be determined from the information given. - ANSWERAnswer C
