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Limits Continuity and Differentiability question

2023 · 30 Jan · Shift 2 · Q28

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JEE Main
Mathematics
Limits Continuity and Differentiability
2023 · 30 Jan · Shift 2 · Q28

Limits Continuity and Differentiability question

2023 · 30 Jan · Shift 2 · Q28

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f, g

and

h

be the real valued functions defined on

\mathbb{R}

as

f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x eq 0 \\ 1, & x=0\end{array}\right.g(x)=\left\{\begin{array}{cc}\frac{\sin (x+1)}{(x+1)}, & x eq-1 \\ 1, & x=-1\end{array}\right.

and

h(x)=2[x]-f(x)

, where

[x]

is the greatest integer

\leq x

. Then the value of

\lim\limits_{x \rightarrow 1} g(h(x-1))

is :

A
1
B
$-1$
C
$\sin (1)$
D
0

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