# Topic: Chapter 9: Differential Calculus Limits and Continuity (Test 2)

Topic: Chapter 9: Differential Calculus Limits and Continuity
Q.1
At x = 3/2 the function f ( x) = | 2x -3 | / 2x -3 is
A. continuous
B. discontinuous
C. differentiable
D. non-zero
Explaination / Solution: Workspace
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Q.2
Let f : R→R be defined by f (x) = then f is
A. discontinuous at x = 1/2
B. continuous at x = 1/2
C. continuous everywhere
D. discontinuous everywhere
Explaination / Solution:
No Explaination.

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Q.3
The function is not defined for x = −1 . The value of f (−1) so that the function extended by this value is continuous is
A. 2/3
B. −2/3
C. 1
D. 0
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Q.4
Let f be a continuous function on [2, 5]. If f takes only rational values for all x and f (3) = 12, then f(4.5) is equal to
A. [f (3) + f (4.5)] / 7.5
B. 12
C. 17.5
D. [f (4.5) − f (3)] / 1.5
Explaination / Solution:

f is a constant function
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Q.5
Let a function f be defined by f (x) = x−|x|  / x for x ≠ 0 and f (0) = 2 . Then f is x
A. continuous nowhere
B. continuous everywhere
C. continuous for all x except x = 1
D. continuous for all x except x = 0
Explaination / Solution: Workspace
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Q.6 A. 1
B. 0
C.
D. −∞
Explaination / Solution: Workspace
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Q.7 A. 2
B. 1
C. −2
D. 0
Explaination / Solution: Workspace
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Q.8 A. 0
B. 1
C. √2
D. does not exist
Explaination / Solution:
No Explaination.

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Q.9 A. 1
B. - 1
C. 0
D. 2
Explaination / Solution: Workspace
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Q.10 is
A. e4
B. e2
C. e3
D. 1