Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Previous in Limits      Next in Limits      

Question Number 75743 by Master last updated on 16/Dec/19

Commented by Master last updated on 16/Dec/19

$$\mathrm{work}\mathrm{without}\mathrm{lopart}$$

Commented by $@ty@m123 last updated on 16/Dec/19

$$Whatismeantbylopart?$$

Commented by abdomathmax last updated on 22/Dec/19

$$letf\left(x\right)={\left(\frac{1}{x}\right)}^{tan\left(x\right)}\Rightarrow f\left(x\right)=e^{-tan\left(x\right)ln\left(x\right)}$$$$tan\left(x\right)lnx\sim xln\left(x\right)(x\to 0)\Rightarrow {lim}_{x\to 0}tanxln\left(x\right)=0$$$$\Rightarrow {lim}_{x\to 0}f\left(x\right)=e^0=1$$

Answered by mr W last updated on 16/Dec/19

$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\underset{x\to 0}{\lim }{\left(\frac{1}{x}\right)}^{\tan x}=\underset{x\to 0}{\lim }{\left[{\left(\frac{1}{x}\right)}^x\right]}^{\frac{\tan x}{x}}={\left(1\right)}^1=1$$$$$$$$similarly$$$$\underset{x\to 0}{\lim }{\left(\frac{1}{x}\right)}^{\sin x}=\underset{x\to 0}{\lim }{\left[{\left(\frac{1}{x}\right)}^x\right]}^{\frac{\sin x}{x}}={\left(1\right)}^1=1$$

Commented by Master last updated on 16/Dec/19

$$\mathrm{thanks}$$

Answered by benjo last updated on 22/Dec/19

Commented by mr W last updated on 22/Dec/19

$$Y={\left(\frac{1}{x}\right)}^{\tan x}$$$$\ln Y=\left(\tan x\right)\ln \left(\frac{1}{x}\right)\ne \ln \left(\tan x\times \frac{1}{x}\right)$$

Commented by john santuy last updated on 24/Dec/19

$$correctsir$$$$lny=\underset{x\to 0}{\stackrel{lim}{}}\frac{ln\left(\frac{1}{x}\right)}{cotx}=\underset{x\to 0}{\stackrel{lim}{}}(-\frac{1}{{csc}^{2}x}).(-\frac{1}{x})$$$$=\underset{x\to 0}{\stackrel{lim}{}}\left(\frac{{sin}^{2}x}{x}\right)=0.nowweget{e}^{lny}=e^0$$$$y=1.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com