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  • The integer for which <img alt="\mathrm{\lim _{x \rightarrow 0} \frac{(\cos x-1)\left(\cos x-e^x\righ

The integer \mathrm{n} for which \mathrm{\lim _{x \rightarrow 0} \frac{(\cos x-1)\left(\cos x-e^x\right)}{x^n}} is a finite non-zero number is

Option: 1

3


Option: 2

1


Option: 3

4


Option: 4

2


Answers (1)

best_answer


\mathrm{ y=\operatorname{Lt}_{x \rightarrow 0}\left(1-\frac{x^2}{2 !}+\frac{x^4}{4 !} \ldots-1\right) \times \left.1-\frac{x^2}{2 !}+\frac{x^4}{4 !} \ldots-\left(1+x+\frac{x^2}{2 !}+\frac{x^3}{3 !} \ldots\right)\right] \div x^n }
\mathrm{ \quad=\underset{x \rightarrow 0}{\operatorname{Lt}}\left(-\frac{x^2}{2}+\frac{x^4}{24} \ldots\right)\left(-x-x^2 \ldots\right) \div x^n }

The least power of \mathrm{ x } in \mathrm{ N^{r}} is \mathrm{3} and if the limit is to be finite then \mathrm{n} must be \mathrm{3.}

Posted by

Irshad Anwar

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