Category: Limits

Question Number 26749 by abdo imad last updated on 28/Dec/17 $$letgive{S}_n=\sum _{1⩽i<j⩽n}\frac{1}{i^2{j}^2}find{lim}_{n->\propto }{S}_n.$$ Commented by abdo imad last updated…

Question Number 26722 by prakash jain last updated on 28/Dec/17 $$\underset{x\to -1^{+}}{\lim }(1+x+x^2+x^3+\dots \mathrm{up}\mathrm{to}\mathrm{\infty })=?$$$$\underset{x\to -1^{-}}{\lim }(1+x+x^2+x^3+\dots \mathrm{up}\mathrm{to}\mathrm{\infty })=?$$ Terms of…

Question Number 92239 by jagoll last updated on 05/May/20 $$\underset{x\to 0}{\lim }\frac{1-\mid \cos 7\mathrm{x}\mid }{1-\mid \tan 5\mathrm{x}\mid }=$$ Commented by john santu last updated on 05/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}^{\mathrm{2}} \:\mathrm{7x}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \:\mathrm{5x}}\:×\:\frac{\mathrm{1}+\mid\mathrm{tan}\:\mathrm{5x}\mid}{\mathrm{1}+\mid\mathrm{cos}\:\mathrm{7x}\mid\:}…

Question Number 92167 by john santu last updated on 05/May/20 $$\underset{x\to \mathrm{\infty }}{\lim }\mathrm{x}-{\mathrm{x}}^2\ln (1+\frac{1}{\mathrm{x}})?$$ Commented by mathmax by abdo last updated on 06/May/20 $${we}\:{have}\:{ln}^{'}…

Question Number 26591 by prakash jain last updated on 27/Dec/17 $$\mathrm{Prove}$$$$\underset{x\to -1}{\lim }(1+x)\ln (1+x)=0$$ Commented by abdo imad last updated on 27/Dec/17 $${let}\:{put}\:\mathrm{1}+{x}={u}\:\:\:\Rightarrow\:{lim}_{{x}−>−\mathrm{1}^{+}…