Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 121051 by mathocean1 last updated on 05/Nov/20

$$\mathrm{show}\mathrm{that}$$$$\underset{\mathrm{x}\to 0}{\lim }\frac{\mathrm{tanx}}{\mathrm{x}}=1$$$$$$$$$$

Answered by 675480065 last updated on 05/Nov/20

$$\mathrm{as}\mathrm{x}\to 0,\mathrm{tanx}\to (\mathrm{x}+\frac{{\mathrm{x}}^3}{3}+0\left({\mathrm{x}}^3\right))$$$$\Rightarrow \underset{x\to 0}{\lim }\frac{\mathrm{tanx}}{\mathrm{x}}=\underset{x\to 0}{\lim }\frac{\mathrm{x}(1+\frac{{\mathrm{x}}^2}{3})}{\mathrm{x}}=\underset{x\to 0}{\lim }(1+\frac{{\mathrm{x}}^2}{3})=1$$

Answered by physicstutes last updated on 05/Nov/20

$$x\to 0,\tan x\to x$$$$\Rightarrow \underset{x\to 0}{\lim }\frac{x}{x}=1\mathrm{QED}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com