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Category: Limits

comment-creer-un-tableau-de-variation-a-partir-de-l-application-

Question Number 164955 by atata01 last updated on 24/Jan/22 $$\mathrm{comment}\:\mathrm{creer}\:\mathrm{un}\:\mathrm{tableau}\:\mathrm{de}\:\mathrm{variation}\:\mathrm{a}\:\mathrm{partir}\:\mathrm{de}\:\mathrm{l}'\mathrm{application}? \\ $$ 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-99392

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

lim-x-1-x-2-cot-2-x-

Question Number 99355 by bemath last updated on 20/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:−\mathrm{cot}\:^{\mathrm{2}} \mathrm{x}\:\right)\:=? \\ $$ Commented by john santu last updated on 20/Jun/20 $$\mathrm{maybe}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}}…

lim-x-3-x-9x-2-8-

Question Number 99350 by bemath last updated on 20/Jun/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\mathrm{3}−\mathrm{x}}{\:\sqrt{\mathrm{9x}^{\mathrm{2}} −\mathrm{8}}\:}\:? \\ $$ 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-99348

Question Number 99348 by bobhans last updated on 20/Jun/20 Commented by bemath last updated on 20/Jun/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\mathrm{3x}+\sqrt{\mathrm{x}^{\mathrm{2}} }}{\mathrm{7x}−\mathrm{5}\sqrt{\mathrm{x}^{\mathrm{2}} }}\:=\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\mathrm{3x}−\mathrm{x}}{\mathrm{7x}+\mathrm{5x}} \\ $$$$=\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\mathrm{2x}}{\mathrm{12x}}\:=\:\frac{\mathrm{1}}{\mathrm{6}} \\…

lim-x-2-x-3-x-1-x-

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

if-lim-x-3-x-ax-b-2x-6-1-6-then-a-2b-

Question Number 99341 by bemath last updated on 20/Jun/20 $$\mathrm{if}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{x}−\sqrt{\mathrm{ax}+\mathrm{b}}}{\mathrm{2x}−\mathrm{6}}\:=\:−\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\mathrm{then}\:\mathrm{a}−\mathrm{2b}\:=\: \\ $$ Commented by bobhans last updated on 20/Jun/20 $$\left(\mathrm{1}\right)\:\mathrm{3}−\sqrt{\mathrm{3a}+\mathrm{b}}\:=\:\mathrm{0}\: \\ $$$$\mathrm{9}\:=\:\mathrm{3a}+\mathrm{b}\:\Rightarrow\mathrm{b}\:=\:\mathrm{9}−\mathrm{3a}…