lim-x-0-x-sin-x-x-5-2-

Question Number 84954 by john santu last updated on 17/Mar/20

\lim_{x \to 0} \frac{\sqrt{x} - \sqrt{\sin x}}{x^{\frac{5}{2}}} = ?

Answered by john santu last updated on 17/Mar/20

\lim_{x \to 0} \frac{x - \sin x}{x^{2} \sqrt{x}} \times \frac{1}{\sqrt{x} + \sqrt{\sin x}} =

\lim_{x \to 0} \frac{x - (x - \frac{1}{6} x^{3})}{x^{3} (1 + \sqrt{\frac{\sin x}{x}})} =

\lim_{x \to 0} \frac{\frac{1}{6} x^{3}}{x^{3} (1 + \sqrt{\frac{\sin x}{x}})} = \frac{\frac{1}{6}}{1 + 1} = \frac{1}{12}

Commented by jagoll last updated on 18/Mar/20

waw \dots great

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