If f(x)= ll x, & x n , n I 2, & otherwise . and g(x)= ll x^ 2 +1,… - Vidyadip

MCQ

If $f(x)=\left\{\begin{array}{ll}\sin x, & x \neq n \pi, \quad n \in I \\ 2, & \text { otherwise }\end{array}\right.$ and $g(x)=\left\{\begin{array}{ll}x^{2}+1, & x \neq 0,2 \\ 2, & x=0 \\ 4, & x=2\end{array}\right.$ then $\lim _{x \rightarrow 0}$$g[f(x)]$ is

A
$3$
B
$2$
C
$4$
✓
$1$

✓

Answer

Correct option: D.

$1$

d
$g[f(x)]=\left\{\begin{array}{cc}{[f(x)} & f^{2}+1 \\ 4 & \text { if } f(x) \neq 0,2 \\ 5 & \text { if } f(x)=0\end{array}\right.$

if $f((x))=2$ $g_{0 f(n)}=\left\{\begin{array}{ccc}\sin ^{2} x+1 & \text { if } & x \neq n \pi \\ 5 & \text { if } & x=n \pi\end{array}\right.$

$\lim _{n \rightarrow 0} g_{0} f=\lim _{n \rightarrow 0} \sin ^{2} n+1=$ $1$

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