Category: Limits

Question Number 78021 by jagoll last updated on 13/Jan/20 $$\underset{x\to 0}{\lim }\frac{1}{x^2}\left[{\underset{\frac{\pi }{3}}{\int }}^{x^2+\frac{\pi }{3}}\frac{\cos x}{x}dx\right]=$$ Commented by mr W last updated on 13/Jan/20…

Question Number 143531 by bramlexs22 last updated on 15/Jun/21 $$\underset{x\to +\mathrm{\infty }}{\lim }\frac{2\sqrt{x}+3\sqrt[3]{x}+5\sqrt[5]{x}}{\sqrt{3x-2}+\sqrt[3]{2x-3}}=?$$ Answered by bobhans last updated on 15/Jun/21 Terms of Service Privacy Policy…

Question Number 12382 by tawa last updated on 21/Apr/17 $$\underset{x\to 0}{\lim }\frac{\ln \cos \left(3\mathrm{x}\right)}{\ln \cos \left(2\mathrm{x}\right)}$$ Answered by ajfour last updated on 21/Apr/17 $$=\underset{x\to 0}{\lim }\frac{\ln [1-(1-\cos 3x)]}{\ln [1-(1-\cos 2x)]}$$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left[\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}}…

Question Number 77856 by walidMTS last updated on 11/Jan/20 $$\underset{x\to 0}{lim}\left(\frac{e^x-x-1}{x}\right)$$ Commented by mathmax by abdo last updated on 11/Jan/20 $${we}\:{have}\:{e}^{{x}} =\sum_{{n}=\mathrm{0}}…

Question Number 143339 by bramlexs22 last updated on 13/Jun/21 Commented by justtry last updated on 13/Jun/21 $$maybe0$$ Answered by mathmax by abdo last…