Category: Limits

Question Number 9768 by ridwan balatif last updated on 01/Jan/17 $$\underset{x\to 0}{\lim }\frac{\sin 3x\cos 3x-\sin 3x}{2x^2\tan 2x\cos \frac{1}{2}x}=\dots ?$$ Answered by sandy_suhendra last updated on 01/Jan/17 $$=\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\:\frac{\mathrm{sin3x}\:\left(\mathrm{cos3x}−\mathrm{1}\right)}{\mathrm{2x}^{\mathrm{2}} \:\mathrm{tan2x}\:\mathrm{cos}\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}}…

Question Number 75268 by aliesam last updated on 09/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 75230 by aliesam last updated on 08/Dec/19 Commented by mathmax by abdo last updated on 08/Dec/19 $$e^{\frac{1}{x}}=1+\frac{1}{x}+o\left(\frac{1}{x^2}\right)\Rightarrow x{e}^{\frac{1}{x}}=x+1+o\left(\frac{1}{x}\right)(x\to +\mathrm{\infty })$$$${e}^{\frac{\mathrm{1}}{{x}+\mathrm{1}}} =\mathrm{1}+\frac{\mathrm{1}}{{x}+\mathrm{1}}\:+{o}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}}…

Question Number 9654 by ridwan balatif last updated on 22/Dec/16 $$\underset{x\to 4}{\lim }\frac{\mathrm{ax}+\mathrm{b}-\sqrt{\mathrm{x}}}{\mathrm{x}-4}=\frac{3}{4},\mathrm{a}+\mathrm{b}=\dots ?$$ Answered by prakash jain last updated on 22/Dec/16 $$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{ax}+\mathrm{b}−\sqrt{\mathrm{x}}}{\mathrm{x}−\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{4}},\:\:\mathrm{a}+\mathrm{b}=…? \…

Question Number 9488 by Joel575 last updated on 10/Dec/16 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{\sqrt{2016}+4\sqrt{2016}+9\sqrt{2016}+\dots +x^2\sqrt{2016}}{x^3}$$ Answered by mrW last updated on 10/Dec/16 $$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2016}}×\left(\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{2}^{\mathrm{2}}…