Category: Limits

Question Number 73730 by TawaTawa last updated on 15/Nov/19 Answered by mind is power last updated on 15/Nov/19 $$f\left(x\right)=e^x-e^c-e^c(x-c)$$$$\Rightarrow{f}'\left({x}\right)={e}^{{x}} −{e}^{{c}}…

Question Number 139140 by mathlove last updated on 23/Apr/21 Answered by TheSupreme last updated on 23/Apr/21 $$sin\left(x\right)=x-\frac{x^3}{3}+o\left(x^3\right)$$$${li}\underset{{x}} {{m}}\frac{\mathrm{2019}{x}−\mathrm{2019}{x}+\frac{\mathrm{2019}^{\mathrm{3}} }{\mathrm{3}}{x}^{\mathrm{3}} }{\mathrm{2020}{x}−\mathrm{2020}{x}+\frac{\mathrm{2020}^{\mathrm{3}} }{\mathrm{3}}{x}^{\mathrm{3}}…

Question Number 73570 by Rio Michael last updated on 13/Nov/19 $$f:x\to \{\begin{array}{l}1+x,ifx<1\\ 2x-1,ifx>1\end{array}$$$$investigatetheexistenceandnonexistenceofthe$$$$limitoffatthepointx=1$$ Commented by kaivan.ahmadi last updated on 13/Nov/19 $${lim}_{{x}\rightarrow\mathrm{1}^{−}…

Question Number 73565 by Rio Michael last updated on 13/Nov/19 $$investigatethecontinuityoff,givenby$$$$f:x\to \{\begin{array}{l}1-x,ifx<1\\ 0,ifx=1\\ x^2-3x+2,ifx>1\end{array}$$$$atthepointx=1$$$$$$ Commented by Rio Michael last…

Question Number 73555 by Rio Michael last updated on 13/Nov/19 $$find$$$$a)\underset{x\to -\mathrm{\infty }}{Lim}\frac{ln(1+e^x)}{e^x}$$$$b)\underset{x\to +\mathrm{\infty }}{lim}(\sqrt{x^2+3x}-x)$$$$c)\underset{x\to 0}{lim}\sqrt{x}ln\left(sinx\right)$$$$\left.{d}\right)\:\:\underset{{x}\rightarrow+\infty}…