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  • Evaluate    <img alt="\mathrm{\lim _{x \rightarrow+\infty} \frac{x(1+\sin x)}{x-\sqrt{1+x^2}}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx%20%5Cr

Evaluate    \mathrm{\lim _{x \rightarrow+\infty} \frac{x(1+\sin x)}{x-\sqrt{1+x^2}}}

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

Does not exist


Answers (1)

best_answer

The limit does not exist. Multiply top and bottom by  \mathrm{x+\sqrt{1+x^2}} . The bottom becomes -1 . As to the new top, it is very big if sin x is not close to -1 . However, there are arbitrarily large x such that sin x=-1.

Posted by

rishi.raj

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