Category: Limits

Question Number 161248 by cortano last updated on 15/Dec/21 $$\underset{x\to 0}{\lim }\frac{{(1+\sin {}^{3}x)}^4-{(1+\tan {}^{3}x)}^4}{x^5}=?$$ Answered by bobhans last updated on 15/Dec/21…

Question Number 30175 by abdo imad last updated on 17/Feb/18 $$provethat{u}_n=\sum _{k=1}^n\frac{1}{n+k}isconvergente.$$ Commented by abdo imad last updated on 21/Feb/18 $${we}\:{have}\:{u}_{{n}}…

Question Number 161186 by mathlove last updated on 13/Dec/21 Answered by Rasheed.Sindhi last updated on 13/Dec/21 $$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{\sqrt{2}x+10}{\sqrt{2}x-11}\right)}^{\frac{2x-1}{x+1}}$$$$=\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{\cancel{x}(\sqrt{2}+\frac{10}{x})}{\cancel{x}(\sqrt{2}-\frac{11}{x})}\right)}^{\frac{\cancel{x}(2-\frac{1}{x})}{\cancel{x}(1+\frac{1}{x})}}$$$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{2}}\:+\frac{\mathrm{10}}{{x}}}{\:\sqrt{\mathrm{2}}\:−\frac{\mathrm{11}}{{x}}}\right)^{\frac{\mathrm{2}−\frac{\mathrm{1}}{{x}}}{\mathrm{1}+\frac{\mathrm{1}}{{x}}}} \…

Question Number 95601 by mehran last updated on 26/May/20 $$1z$$$$$$$$1$$ Commented by john santu last updated on 26/May/20 $$\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{meant}?…

Question Number 161111 by cortano last updated on 12/Dec/21 $$\underset{x\to 0}{\lim }\frac{x^2+2\cos x-2}{x^4}=\frac{1}{a}$$$$a=?$$ Commented by blackmamba last updated on 12/Dec/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}}…