Category: Limits

Question Number 63959 by meme last updated on 11/Jul/19 $$li{\underset{x\to +\mathrm{\infty }}{me}}^{xln(1+\frac{1}{x})}$$ Commented by Prithwish sen last updated on 11/Jul/19 $$\:\mathrm{li}\underset{\mathrm{x}\rightarrow\infty} {\mathrm{m}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \rightarrow\:\mathrm{e} \…

Question Number 63922 by raj last updated on 11/Jul/19 $$\mathrm{if}f\left(x\right)=\{\begin{array}{ll}\frac{\log (1+2ax)-\log (1-bx)}{x}& x\ne 0\\ k& x=0\end{array}$$$$\mathrm{is}\mathrm{continuous}\mathrm{at}x=0\mathrm{then}k=?$$ Commented by kaivan.ahmadi last updated on 11/Jul/19 $${lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right)\overset{{hop}} {=}{lim}_{{x}\rightarrow\mathrm{0}\:\:} \frac{\mathrm{2}{a}}{{ln}\mathrm{10}×\left(\mathrm{1}+\mathrm{2}{ax}\right)}−\frac{−{b}}{{ln}\mathrm{10}×\left(\mathrm{1}−{bx}\right)}=…

Question Number 63920 by raj last updated on 11/Jul/19 $$\mathrm{If}\alpha ,\beta \mathrm{are}\mathrm{root}\mathrm{of}\mathrm{quadratic}\mathrm{equation}$$$${ax}^2+bx+c\mathrm{then}$$$$\underset{x\to \alpha }{\lim }\frac{1-\cos ({ax}^2+bx+c)}{{(x-\alpha )}^2}=?$$ Commented by Prithwish sen last…

Question Number 129387 by Study last updated on 15/Jan/21 $$li\underset{x\to 0}{m}{\left(cosx\right)}^{logx}=???$$ Commented by Study last updated on 15/Jan/21 $$whowillsolve?$$ Answered…

Question Number 63710 by aliesam last updated on 07/Jul/19 Commented by mathmax by abdo last updated on 08/Jul/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{{n}}} {n}^{\mathrm{2}} \:{x}^{{x}+\mathrm{1}} \:{ex}\:\Rightarrow{A}_{{n}} =\int_{\mathrm{0}}…