Category: Limits

Question Number 54409 by pooja24 last updated on 03/Feb/19 $$li\underset{x\to \mathrm{\infty }}{m}\sqrt{(x^2+x+1)}-x=?$$$$plssolvethis$$$$$$ Commented by maxmathsup by imad last updated…

Question Number 185438 by mathlove last updated on 21/Jan/23 $$\underset{x\to 0}{\lim }\frac{a^x\sin \left(ax\right)-b^x\sin \left(bx\right)}{c^x\sin \left(cx\right)-d^x\sin dx)}=?$$ Answered by hmr last updated on 21/Jan/23 $${L}'\:{Hopital}\:{Rule}:…

Question Number 185405 by greougoury555 last updated on 21/Jan/23 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{{(x+2)}^{1/x}-x^{1/x}}{{(x+3)}^{1/x}-x^{1/x}}=?$$ Answered by Frix last updated on 22/Jan/23 $$=\underset{{t}\rightarrow\mathrm{0}^{+}…

Question Number 119867 by Study last updated on 27/Oct/20 $$li\underset{x\to \mathrm{\infty }}{m}\frac{{(1+\frac{1}{2n})}^n-\sqrt{e}}{{(1+\frac{2}{n})}^n-e^2}=???$$ Commented by Dwaipayan Shikari last updated on 27/Oct/20 $$\frac{\mathrm{1}}{\mathrm{16}}{e}^{−\frac{\mathrm{3}}{\mathrm{2}}}…

Question Number 119725 by bemath last updated on 26/Oct/20 $$\underset{x\to \frac{\pi }{4}}{\lim }\frac{4\sqrt{2}-{(\cos x+\sin x)}^5}{{(\cos x-\sin x)}^2}=?$$ Commented by bemath last updated on 26/Oct/20 $$comparevia{L}^{\prime }Hopital$$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}}…