If f(x)= (e^ x-3 -1 ) (x-2) , then _ x 3 f(x)= - Vidyadip

MCQ

If $f(x)=\frac{\sin \left(e^{x-3}-1\right)}{\log (x-2)}$, then $\lim _{x \rightarrow 3} f(x)=$

A
-2
B
-1
✓
1
D
$0$

✓

Answer

Correct option: C.

1

(C)
$\lim _{x \rightarrow 3} f (x)=\lim _{x \rightarrow 3} \frac{\sin \left( e ^{x-3}-1\right)}{\log (x-2)}$
$=\lim _{h \rightarrow 0} \frac{\sin \left(e^h-1\right)}{\log (1+h)}$
$=\lim _{h \rightarrow 0} \frac{\sin \left(e^h-1\right)}{e^h-1} \cdot \frac{e^h-1}{h} \cdot \frac{h}{\log (1+h)}=1$

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