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Limits Continuity and Differentiability question

2022 · 28 Jul · Shift 2 · Q25

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JEE Main
Mathematics
Limits Continuity and Differentiability
2022 · 28 Jul · Shift 2 · Q25

Limits Continuity and Differentiability question

2022 · 28 Jul · Shift 2 · Q25

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

The function

f: \mathbb{R} \rightarrow \mathbb{R}

defined by

f(x)=\lim\limits_{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}

is continuous for all x in :

A
$R-\{-1\}$
B
$\mathbb{R}-\{-1,1\}$
C
$R-\{1\}$
D
$R-\{0\}$

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