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  • Evaluate   <img alt="\mathrm{\lim _{x \rightarrow 0} \frac{x \cos x-\sin x}{x^2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx%20%5Crightarrow%200%7D%2

Evaluate   \mathrm{\lim _{x \rightarrow 0} \frac{x \cos x-\sin x}{x^2}}

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

-1


Answers (1)

best_answer

\mathrm{L=\lim _{x \rightarrow 0} \frac{x \cos x-\sin x}{x^2} \\ }

\mathrm{=\lim _{x \rightarrow 0} \frac{x\left[1-\frac{x^2}{2 !}+\frac{x^4}{4 !}-\ldots\right]-\left(x-\frac{x^3}{3 !}+\frac{x^5}{5 !}-\ldots\right)}{x^2} \\ }

\mathrm{=0 }

Posted by

HARSH KANKARIA

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