Category: Limits

Question Number 164955 by atata01 last updated on 24/Jan/22 $$\mathrm{comment}\mathrm{creer}\mathrm{un}\mathrm{tableau}\mathrm{de}\mathrm{variation}\mathrm{a}\mathrm{partir}\mathrm{de}{\mathrm{l}}^{\prime }\mathrm{application}?$$ Commented by Ar Brandon last updated on 24/Jan/22 $$\begin{array}{|c|c|c|}{{x}}&\hline{−\pi\:\:\:\:\:\:\:\:\:\:\:−\frac{\pi}{\mathrm{2}}}&\hline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}}&\hline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\pi}{\mathrm{2}}}&\hline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\pi}\{\mathrm{f}\:'\left({x}\right)}&\hline{\:\:\:\:\:\:\:\:\:\:\:\:−}&\hline{\:\:\:\:\:\:\:\:\:+}&\hline{\:\:\:\:\:\:\:\:\:\:+}&\hline{\:\:\:\:\:\:\:−}\{\mathrm{f}\left({x}\right)}&\hline{\overset{\mathrm{0}} {\:}\:\:\:\:\:\:\:\:\:\searrow\:\:_{\:\:\:\:\:−\mathrm{1}} }&\hline{\:\:\:\:\:\:\:\:\:\nearrow^{\:\:\:\:\:\mathrm{0}} }&\hline{\underset{\mathrm{0}} {\:}\:\:\:\:\:\:\:\nearrow^{\:\:\:\:\:\:\mathrm{1}}…

Question Number 99392 by AwaisAhmed last updated on 20/Jun/20 Commented by PRITHWISH SEN 2 last updated on 21/Jun/20 $$\mathrm{To}\mathrm{be}\mathrm{continuous}$$$$4\mathrm{b}=-2\Rightarrow \mathbf{b}=-\frac{1}{2}$$ Answered by…

Question Number 99350 by bemath last updated on 20/Jun/20 $$\underset{x\to -\mathrm{\infty }}{\lim }\frac{3-\mathrm{x}}{\sqrt{{9\mathrm{x}}^2-8}}?$$ Commented by bobhans last updated on 20/Jun/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{−\mathrm{x}\left(\mathrm{1}−\frac{\mathrm{3}}{\mathrm{x}}\right)}{−\mathrm{x}\sqrt{\mathrm{9}−\frac{\mathrm{8}}{\mathrm{x}^{\mathrm{2}} }}}\:=\:\frac{\mathrm{1}}{\mathrm{3}} \…

Question Number 99344 by bemath last updated on 20/Jun/20 $$\underset{x\to \mathrm{\infty }}{\lim }{(2^{\mathrm{x}}+3^{\mathrm{x}})}^{\frac{1}{\mathrm{x}}}?$$ Answered by abdomsup last updated on 20/Jun/20 $${let}\:{f}\left({x}\right)=\left(\mathrm{2}^{{x}} \:+\mathrm{3}^{{x}}…

Question Number 99340 by bobhans last updated on 20/Jun/20 $$\mathrm{Given}\mathrm{a}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right)=\{\begin{array}{l}2\mathrm{x}-\mathrm{a},\mathrm{x}<-3\\ \mathrm{ax}+\mathrm{b},-3⩽\mathrm{x}⩽3\\ \mathrm{b}-5\mathrm{x},\mathrm{x}>3\end{array}$$$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{a}\mathrm{and}\mathrm{b}\mathrm{such}\mathrm{that}$$$$\underset{x\to -3}{\lim f}\left(\mathrm{x}\right)\mathrm{and}\underset{x\to 3}{\lim }\mathrm{f}\left(\mathrm{x}\right)\mathrm{exist}$$ Commented by PRITHWISH SEN 2 last updated…