The value of lim x -5sin x-2 x-1-cos x-1-x2 is

The correct option is A 2lim_x →∞5^sin x + 2x + 1cos x √(1 + x^2)=lim_x →∞(5^sin x + 2x + 1)x(cos x √(1 + x^2))x = nbsp;lim_x →∞5^sin xx + 2 + 1xcos xx ...

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Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

The value of ...

Question

The value of $lim x \to \infty \frac{5^{sin x} + 2 x + 1}{cos x - \sqrt{1 + x^{2}}}$ is

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Solution

The correct option is A $- 2$
$lim x \to \infty \frac{5^{sin x} + 2 x + 1}{cos x - \sqrt{1 + x^{2}}} = lim x \to \infty \frac{\frac{(5^{sin x} + 2 x + 1)}{x}}{\frac{(cos x - \sqrt{1 + x^{2}})}{x}}$
$= lim x \to \infty \frac{\frac{5^{sin x}}{x} + 2 + \frac{1}{x}}{\frac{cos x}{x} - \sqrt{\frac{1}{x^{2}} + 1}} = \frac{2}{- \sqrt{1}} = \frac{2}{- 1} = - 2$

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The value of limx→∞5sin x+2x+1cos x−√1+x2 is

The correct option is A −2limx→∞5sin x+2x+1cos x−√1+x2=limx→∞(5sin x+2x+1)x(cos x−√1+x2)x =limx→∞5sin xx+2+1xcos xx−√1x2+1=2−√1=2−1=−2

The value of $lim x \to \infty \frac{5^{sin x} + 2 x + 1}{cos x - \sqrt{1 + x^{2}}}$ is