lim _x arrow 0 frac3^sin x-2^tan xsin x=

Correct answer: (D) log _e 3/2. lim _x arrow 0 frac3^sin x-2^tan xsin x =lim _x arrow 0 frac3^sin x-1- (2^tan x-1 )sin x=ln 3-ln 2=ln (3/2 )

Q101 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics

$\lim _{x \rightarrow 0} \frac{3^{\sin x}-2^{\tan x}}{\sin x}=$

A
0
B
1
C
$\log e 6$
Correct answer
D
$\log _e \frac{3}{2}$

Solution

$\lim _{x \rightarrow 0} \frac{3^{\sin x}-2^{\tan x}}{\sin x}$ $=\lim _{x \rightarrow 0} \frac{3^{\sin x}-1-\left(2^{\tan x}-1\right)}{\sin x}=\ln 3-\ln 2=\ln \left(\frac{3}{2}\right)$

Hence, the correct answer is option: 'D'.

$\lim _{x \rightarrow 0} \frac{3^{\sin x}-2^{\tan x}}{\sin x}=$

Solution

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