Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

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

Commented by Ml last updated on 09/Jan/23

$$\mathrm{please}\mathrm{solution}????$$

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

$$=\underset{x\to 0}{\lim }\frac{\sin x^3}{x^3}\times \frac{\tan x}{x}\times {\left(\frac{\sin \frac{x}{2}}{\frac{x}{2}}\right)}^2\times {\left(\frac{x}{\sin x}\right)}^5\times \frac{x^{\frac{1}{6}}}{2{(x+x^{\frac{1}{3}})}^{\frac{1}{2}}}$$$$=\underset{x\to 0}{\lim }\frac{x^{\frac{1}{6}}}{2{(x+x^{\frac{1}{3}})}^{\frac{1}{2}}}$$$$=\underset{x\to 0}{\lim }\frac{1}{2{(x^{\frac{4}{3}}+1)}^{\frac{1}{2}}}$$$$=\frac{1}{2}$$

Answered by qaz last updated on 10/Jan/23

$$\underset{x\to 0^{+}}{lim}\frac{\sin x^3\tan x(1-\cos x)}{\sqrt{x+\sqrt[3]{x}}\left(\sqrt[6]{x^5}\sin {}^{5}x\right)}$$$$=\underset{x\to 0^{+}}{lim}\frac{x^3\cdot x\cdot \frac{1}{2}{x}^2}{\sqrt[2]{\sqrt[3]{x}}\cdot \sqrt[6]{x^5}\cdot x^5}$$$$=\frac{1}{2}$$$$-----------$$$$x\to 0^{+},sin{x}^3\sim x^{3}tanx\sim x1-\cos x\sim \frac{1}{2}{x}^2$$$$\sqrt{x+\sqrt[3]{x}}\sim \sqrt[2]{\sqrt[3]{x}}\sin {}^{5}x\sim x^5$$

Commented by Ml last updated on 09/Jan/23

$$\mathrm{step}\mathrm{by}\mathrm{step}????$$

Answered by cortano1 last updated on 10/Jan/23

Terms of Service

Privacy Policy

Contact: info@tinkutara.com