A) \[4\text{ }log\text{ }5\]
B) \[2\text{ }log\text{ }5\]
C) \[\frac{1}{2}log\text{ }5\]
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{x({{5}^{x}}-1)}{1-\cos x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{x\left[ 1+x\log +\frac{{{x}^{2}}}{2!}{{(\log 5)}^{2}}+....-1 \right]}{1-\left( 1-\frac{{{x}^{2}}}{2!}+\frac{{{x}^{4}}}{4!}-.... \right)}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\frac{{{x}^{2}}}{2!}[2\log 5+x{{(\log 5)}^{2}}+....]}{\frac{{{x}^{2}}}{2!}\left( 1-\frac{{{x}^{2}}}{12}+.... \right)}\] \[=2\log 5\]
You need to login to perform this action.
You will be redirected in
3 sec
