Question Number 15195 by Joel577 last updated on 08/Jun/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{2}{x}\:−\:\mathrm{5}}{\mathrm{2}{x}\:+\:\mathrm{1}}\right)^{{x}\:+\:\mathrm{3}} \\ $$ Commented by Joel577 last updated on 08/Jun/17 $$=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}\:−\:\frac{\mathrm{6}}{\mathrm{2}{x}\:+\:\mathrm{1}}\right)^{{x}\:+\:\mathrm{3}} \\ $$$$=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left\{\left[\left(\mathrm{1}\:−\:\frac{\mathrm{6}}{\mathrm{2}{x}\:+\:\mathrm{1}}\right)^{−\:\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{\mathrm{6}}}…
Question Number 146263 by bemath last updated on 12/Jul/21 $$\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\left(−\mathrm{2}{x}+\mathrm{1}−\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{8}}\right)=? \\ $$ Answered by gsk2684 last updated on 12/Jul/21 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\left(−\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} −\left(\mathrm{4}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{8}\right)}{−\mathrm{2}{x}+\mathrm{1}+\sqrt{\mathrm{4}{x}^{\mathrm{2}}…
Question Number 15186 by Joel577 last updated on 08/Jun/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{x}\:+\:\mathrm{3}}{{x}\:−\mathrm{1}}\right)^{{x}} \\ $$ Commented by mrW1 last updated on 08/Jun/17 $$\mathrm{yes},\:\mathrm{correct}. \\ $$ Commented by…
Question Number 80718 by TawaTawa last updated on 05/Feb/20 $$\mathrm{Evaluate}:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{x}}{\mid\mathrm{x}\mid} \\ $$ Commented by mind is power last updated on 05/Feb/20 $$\mid{x}\mid=\begin{cases}{{x},\:\:\:\:\:\:\:\:{x}>\mathrm{0}}\\{−{x}\:\:\:,{x}<\mathrm{0}}\end{cases} \\ $$$$\Rightarrow\underset{{x}\rightarrow\mathrm{0}^{+}…
Question Number 15181 by Joel577 last updated on 08/Jun/17 $${f}\left({x}\right)\:=\:\frac{\left({px}\:+\:{q}\right)\:.\:\mathrm{sin}\:\mathrm{2}{x}}{{ax}\:+\:{b}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\mathrm{2}\:\:\:\mathrm{and}\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:{a},{b},{p},{q}\:\: \\ $$ Answered by ajfour last updated on 08/Jun/17…
Question Number 80690 by ahmadshahhimat775@gmail.com last updated on 05/Feb/20 Commented by jagoll last updated on 05/Feb/20 $$\underset{{x}\rightarrow{e}} {\mathrm{lim}}\:\frac{{xlnx}−{x}}{\mathrm{2}−\mathrm{2}{lnx}}\:=\underset{{x}\rightarrow{e}} {\mathrm{lim}}\:\frac{{x}\left({lnx}\:−\mathrm{1}\right)}{−\mathrm{2}\left({lnx}−\mathrm{1}\right)}= \\ $$$$−\frac{{e}}{\mathrm{2}} \\ $$ Commented by…
Question Number 80688 by ahmadshahhimat775@gmail.com last updated on 05/Feb/20 Commented by jagoll last updated on 05/Feb/20 $$\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 80689 by ahmadshahhimat775@gmail.com last updated on 05/Feb/20 Commented by john santu last updated on 05/Feb/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{20}\left({x}−\mathrm{1}\right)}{{ln}\left(\mathrm{2}{x}−\mathrm{1}\right)}=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{20}}{\left(\frac{\mathrm{2}}{\left.\mathrm{2}{x}−\mathrm{1}\right)}\right)} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{10}\left(\mathrm{2}{x}−\mathrm{1}\right)}{\mathrm{1}}=\mathrm{10} \\ $$…
Question Number 80670 by jagoll last updated on 05/Feb/20 $$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{{e}^{\mathrm{sin}\:{x}} −\mathrm{1}}{{x}−\pi}=? \\ $$ Commented by jagoll last updated on 05/Feb/20 $$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}.{e}^{\mathrm{sin}\:{x}} }{\mathrm{1}}=\:−\mathrm{1} \\…
Question Number 80653 by jagoll last updated on 05/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:{x}}{{x}}\right)^{\frac{\mathrm{3}}{{x}^{\mathrm{2}} }} \\ $$ Commented by john santu last updated on 05/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\left(\frac{\mathrm{sin}\:{x}}{{x}}−\mathrm{1}\right)\right)^{\frac{\mathrm{3}}{{x}^{\mathrm{2}} }}…