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Limits Continuity and Differentiability question

2017 · Shift 2 · Q30

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JEE Advanced
Mathematics
Limits Continuity and Differentiability
2017 · Shift 2 · Q30

Limits Continuity and Differentiability question

2017 · Shift 2 · Q30

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −2

Let

f(x) = {{1 - x(1 + |1 - x|)} \over {|1 - x|}}\cos \left( {{1 \over {1 - x}}} \right)

for x

e

1. Then

A
$\mathop {\lim }\limits_{x \to {1^ + }} f(x)$ = 0
B
$\mathop {\lim }\limits_{x \to {1^ - }} f(x)$ does not exist
C
$\mathop {\lim }\limits_{x \to {1^ - }} f(x)$ = 0
D
$\mathop {\lim }\limits_{x \to {1^ + }} f(x)$ does not exist

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