Category: Limits

Question Number 99947 by bemath last updated on 24/Jun/20 $$\underset{x\to \mathrm{\infty }}{\lim }x(5^{\frac{1}{x}}-1)=?$$ Commented by bobhans last updated on 24/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{x}}} −\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{x}}}\:=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5}^{\mathrm{t}}…

Question Number 99936 by student work last updated on 24/Jun/20 $$\mathrm{li}\underset{\mathrm{x}\to 0}{\mathrm{m}}\frac{{(1+\mathrm{x})}^{\mathrm{k}}-1}{\mathrm{x}}=?$$$$\mathrm{help}\mathrm{me}$$ Commented by bemath last updated on 24/Jun/20 $$\mathrm{for}\:\mathrm{k}\:>\:\mathrm{0}\:\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}}…

Question Number 34375 by rahul 19 last updated on 05/May/18 $$\mathit{T}hevalueof$$$${lim}_{x\to \frac{\pi }{2}}\frac{\left[\frac{x}{2}\right]}{\log \left(\sin x\right)}=?$$$$[.]=greatestintegerfunction.$$ Answered by MJS last updated on 05/May/18…

Question Number 34367 by rahul 19 last updated on 05/May/18 $$\mathbf{Evaluate}$$$${\lim }_{\mathrm{n}\to \mathrm{\infty }}(\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\dots ..+\frac{n}{n^2+n^2}).$$ Answered by tanmay.chaudhury50@gmail.com…

Question Number 99720 by bobhans last updated on 23/Jun/20 $$\underset{x\to 0}{\lim }\frac{1}{{\mathrm{x}}^2}-\frac{1}{\tan {}^2\mathrm{x}}?$$ Commented by john santu last updated on 23/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:^{\mathrm{2}}…