A) \[{{e}^{4}}\]
B) \[{{e}^{2}}\]
C) \[{{e}^{3}}\]
D) e
Correct Answer: A
Solution :
\[L=\underset{x\to 0}{\mathop{Lim}}\,\,\frac{{{\int\limits_{0}^{x}{({{t}^{2}}+{{e}^{{{t}^{2}}}})}}^{\frac{1}{1-\cos \,tr}}}dt}{x}\,\,\left( \frac{0}{0} \right)\] \[=\underset{x\to 0}{\mathop{Lim}}\,\,\,{{\left( {{e}^{{{x}^{2}}}}\,+{{x}^{2}} \right)}^{\frac{1}{1-\cos x}}}\] \[={{e}^{\underset{x\to 0}{\mathop{Lim}}\,\,\frac{{{e}^{{{x}^{2}}}}\,+{{x}^{2}}-1}{\frac{(1-\cos x)}{{{x}^{2}}}.\,{{x}^{2}}}\,}}\,={{e}^{2\underset{x\to 0}{\mathop{Lim}}\,\,\left( \frac{{{e}^{{{x}^{2}}}}-1}{{{x}^{2}}}+1 \right)}}={{e}^{4}}\]
You need to login to perform this action.
You will be redirected in
3 sec
