Question-184620

Question Number 184620 by Ml last updated on 09/Jan/23

Commented by Ml last updated on 09/Jan/23

please solution ? ? ? ?

Answered by mr W last updated on 09/Jan/23

= \lim_{x \to 0} \frac{\sin x^{3}}{x^{3}} \times \frac{\tan x}{x} \times {(\frac{\sin \frac{x}{2}}{\frac{x}{2}})}^{2} \times {(\frac{x}{\sin x})}^{5} \times \frac{x^{\frac{1}{6}}}{2 {(x + x^{\frac{1}{3}})}^{\frac{1}{2}}}

= \lim_{x \to 0} \frac{x^{\frac{1}{6}}}{2 {(x + x^{\frac{1}{3}})}^{\frac{1}{2}}}

= \lim_{x \to 0} \frac{1}{2 {(x^{\frac{4}{3}} + 1)}^{\frac{1}{2}}}

= \frac{1}{2}

Answered by qaz last updated on 10/Jan/23

\underset{x \to 0^{+}}{l i m} \frac{\sin x^{3} \tan x (1 - \cos x)}{\sqrt{x + \sqrt[3]{x}} (\sqrt[6]{x^{5}} \sin^{5} x)}

= \underset{x \to 0^{+}}{l i m} \frac{x^{3} \cdot x \cdot \frac{1}{2} x^{2}}{\sqrt[2]{\sqrt[3]{x}} \cdot \sqrt[6]{x^{5}} \cdot x^{5}}

= \frac{1}{2}

- - - - - - - - - - -

x \to 0^{+}, s i n x^{3} \sim x^{3} t a n x \sim x 1 - \cos x \sim \frac{1}{2} x^{2}

\sqrt{x + \sqrt[3]{x}} \sim \sqrt[2]{\sqrt[3]{x}} \sin^{5} x \sim x^{5}

Commented by Ml last updated on 09/Jan/23

step by step ? ? ? ?

Answered by cortano1 last updated on 10/Jan/23

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