Category: Limits

Question Number 34464 by rahul 19 last updated on 06/May/18 $$\mathit{E}valuate$$$$\underset{x\to 0^{+}}{\lim }{x}^m{\left(logx\right)}^n,m,n\in \mathbb{N}$$ Answered by MJS last updated on…

Question Number 34439 by rahul 19 last updated on 06/May/18 $$\underset{x\to \mathrm{\infty }}{\lim }{(-1)}^{x-1}\sin \left(\pi \sqrt{x^2+0.5x+1}\right),$$$$wherex\in \mathbb{N}.$$ Answered by MJS last updated on 07/May/18…

Question Number 99968 by bobhans last updated on 24/Jun/20 $$\underset{x\to 0^{+}}{\lim }{\left(\sin \mathrm{x}\right)}^{\frac{1}{\ln \left(\mathrm{x}\right)}}=?$$ Commented by bobhans last updated on 24/Jun/20 $$=\mathrm{e}^{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{ln}\left(\mathrm{x}\right)}} =\:\mathrm{e}^{\underset{{x}\rightarrow\mathrm{0}}…

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}}…