Question

plz answer this question

Answer 1

Hope it helps you
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Answer 2

[tex]\lim_{x \to \infty} (x-\sqrt{x^{2}+x}) =  \lim_{x \to \infty} (x-\sqrt{x^{2}+x})\frac{x+\sqrt{x^{2}+x} }{x+\sqrt{x^{2}+x} }  = \lim_{x \to \infty} \frac{x^{2}-(x^{2}+x)}{x+\sqrt{ x^{2}+x}}[/tex]

$\lim_{x \to \infty} \frac{-x}{x\sqrt{1+\frac{1}{x} }+x }  = \lim_{x \to \infty} \frac{-x}{x(\sqrt{1+\frac{1}{x} }+1) }  = \lim_{x \to \infty} \frac{-1}{\sqrt{1+\frac{1}{x} } +1}$

when x tends to infinity,1/x tends to zero.

so limit is  ,,,,,,,,,

-1/(√1+1)

=-1/2