Category: Limits

Question Number 158037 by Tawa11 last updated on 30/Oct/21 $$\left(1\right)\underset{\mathrm{z}\to -\mathrm{i}}{\lim }\frac{\mathrm{z}-\mathrm{i}}{{\mathrm{z}}^2+1}$$$$\left(2\right)\underset{\mathrm{z}\to -\mathrm{i}}{\lim }\frac{\mathrm{z}+\mathrm{i}}{{\mathrm{z}}^2+1}$$$$\left(3\right)\underset{\mathrm{z}\to \mathrm{i}}{\lim }\frac{{2\mathrm{z}}^2-\mathrm{zi}+1}{\mathrm{z}-\mathrm{i}}$$ Terms of Service…

Question Number 158017 by cortano last updated on 30/Oct/21 Commented by tounghoungko last updated on 31/Oct/21 $$\underset{x\to 0^{-}}{\lim }f\left(x\right)=\underset{x\to 0^{+}}{\lim }f\left(x\right)$$$$\Rightarrow\underset{{x}\rightarrow\mathrm{0}^{\:+} } {\mathrm{lim}}\left({x}^{\frac{\mathrm{7}}{\mathrm{9}}}…

Question Number 92423 by mhmd last updated on 06/May/20 $${lim}_{x\Rightarrow \mathrm{\infty }}\frac{4(x+3)!-x!}{x[(x+2)!-(x-1)!]}$$ Answered by john santu last updated on 07/May/20 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{4(\mathrm{x}+3)(\mathrm{x}+2)(\mathrm{x}+1)\mathrm{x}!-\mathrm{x}!}{\mathrm{x}(\mathrm{x}+2)(\mathrm{x}+1)\mathrm{x}!-\mathrm{x}(\mathrm{x}-1)!}$$$$\underset{{x}\rightarrow\infty}…

Question Number 157942 by mathlove last updated on 30/Oct/21 Commented by cortano last updated on 30/Oct/21 $$\left(1\right)x+2x+3x+\dots +nx=\frac{n}{2}(nx+x)$$$$\left(2\right)\underset{x\to 0}{\lim }\frac{(1+\frac{x}{2})(1+\frac{2x}{2})(1+\frac{3x}{2})\dots (1+\frac{nx}{2})-1}{\frac{n}{2}(nx+x)}$$$$L=\frac{2}{n(n+1)}.\underset{x\to 0}{\lim }\frac{(\frac{1}{2}+\frac{2}{2}+\frac{3}{2}+\dots +\frac{n}{2})x}{x}$$$${L}=\frac{\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}.\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}\right)…

Question Number 26768 by abdo imad last updated on 29/Dec/17 $$findthenatureof{U}_n=\sum _{p=0}^{p=n}\frac{1}{C_n^p}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com