Category: Limits

Question Number 78682 by Omer Alattas last updated on 19/Jan/20 Commented by mathmax by abdo last updated on 19/Jan/20 $$wehave{\left(sinx\right)}^x=e^{xln\left(sinx\right)}andxln\left(sinx\right)\sim xlnx(x\to 0)\Rightarrow$$$${lim}_{{x}\rightarrow\mathrm{0}^{+} }…

Question Number 78635 by Pratah last updated on 19/Jan/20 Commented by john santu last updated on 19/Jan/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\underset{{n}} {\overset{\mathrm{2}{n}} {\int}}\:\left(\frac{{x}}{{x}^{\mathrm{5}} +\mathrm{1}}\right){dx}\:}{{n}^{−\mathrm{3}} }\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\frac{\mathrm{2}{n}}{\mathrm{32}{n}^{\mathrm{5}} +\mathrm{1}}\right).\mathrm{2}−\left(\frac{{n}}{{n}^{\mathrm{5}}…

Question Number 413 by 123456 last updated on 25/Jan/15 $$\underset{(x,y)\to (0,0)}{\lim }\frac{(x+y)(x^2-y^2)}{\sqrt{x^2+y^2}}$$ Answered by prakash jain last updated on 31/Dec/14…

Question Number 394 by prakash jain last updated on 27/Dec/14 $$f\left(x\right)=\underset{i=1}{\sum ^{\mathrm{\infty }}}{a}_i{x}^i$$$$a_i\mathrm{A}\mathrm{constant}\mathrm{independent}\mathrm{of}x$$$$\mathrm{I}s\mathrm{the}\mathrm{below}\mathrm{statement}\mathrm{correct}?$$$$\underset{x\to 0}{\lim }f\left(x\right)=0$$$$\mathrm{If}\:\mathrm{not}\:\mathrm{give}\:\mathrm{an}\:\mathrm{example}. \…

Question Number 131444 by rs4089 last updated on 04/Feb/21 Answered by Olaf last updated on 05/Feb/21 $$\mathrm{polar}\mathrm{coordinates}:$$$$\frac{{xy}+\mathrm{2}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:=\:\frac{{r}\mathrm{cos}\theta.{r}\mathrm{sin}\theta+\mathrm{2}}{{r}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \theta+{r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \theta}…