Category: Limits

Question Number 130696 by LYKA last updated on 28/Jan/21 Answered by mathmax by abdo last updated on 28/Jan/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\mathrm{y}^{\mathrm{2}} }\:\Rightarrow\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \mathrm{f}\left(\mathrm{x},\mathrm{x}\right)=\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \frac{\mathrm{x}^{\mathrm{2}}…

Question Number 130596 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{For}\mathrm{what}\mathrm{value}\mathrm{of}\mathrm{a}\mathrm{and}\mathrm{b}\mathrm{is}\mathrm{the}\mathrm{following}$$$$\mathrm{equation}\mathrm{true}?$$$$\underset{x\to 0}{\lim }(\frac{\sin 2\mathrm{x}}{{\mathrm{x}}^3}+\mathrm{a}+\frac{\mathrm{b}}{{\mathrm{x}}^2})=0.$$ Answered by mr W last updated…

Question Number 130541 by EDWIN88 last updated on 26/Jan/21 $$\underset{x\to 0}{\lim }\frac{e^{-x^2/2}-\cos x}{x^3\tan x}=?$$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}}…

Question Number 130483 by benjo_mathlover last updated on 26/Jan/21 Answered by EDWIN88 last updated on 10/Feb/21 $$\left(5\right)\underset{x\to -1}{\lim cos}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\cos \underset{x\to -1}{\lim f}\left(\mathrm{x}\right)=\cos (-1)=\cos 1$$ Terms of Service Privacy…

Question Number 130406 by john_santu last updated on 25/Jan/21 $$\underset{x\to \pi /2}{\lim }\cos (2x+\sin (\frac{3\pi }{2}+x)=?$$ Commented by Dwaipayan Shikari last updated on 25/Jan/21 $$-1$$ Answered…