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Category: Limits

lim-x-0-csc-2-2x-1-4x-2-

Question Number 105584 by bemath last updated on 30/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\mathrm{csc}^{\mathrm{2}} \left(\mathrm{2}{x}\right)−\frac{\mathrm{1}}{\mathrm{4}{x}^{\mathrm{2}} }\:\right]? \\ $$ Answered by bobhans last updated on 30/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)}−\frac{\mathrm{1}}{\mathrm{4}{x}^{\mathrm{2}}…

calculate-0-sin-x-x-dx-

Question Number 105545 by 4635 last updated on 29/Jul/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:{x}}{{x}}{dx} \\ $$ Answered by Ar Brandon last updated on 29/Jul/20 $$\mathrm{Let}\:\mathrm{f}\left(\mathrm{a}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sinx}}{\mathrm{x}}\centerdot\mathrm{e}^{−\mathrm{ax}}…

lim-x-0-1-1-1-x-1-1-1-x-x-

Question Number 171079 by greougoury555 last updated on 07/Jun/22 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}−{x}}}}−\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}}}}}{{x}}=? \\ $$ Commented by benhamimed last updated on 07/Jun/22 $$\frac{−\mathrm{1}}{\mathrm{24}} \\ $$ Commented by…

Given-lim-x-5-f-x-a-x-5-8-lim-x-5-x-2-ax-b-f-x-a-1-find-the-value-of-b-23-

Question Number 105383 by bemath last updated on 28/Jul/20 $$\mathcal{G}{iven}\:\begin{cases}{\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\frac{{f}\left({x}\right)−{a}}{{x}−\mathrm{5}}\:=\:\mathrm{8}}\\{\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −{ax}+{b}}{{f}\left({x}\right)−{a}}\:=\:\mathrm{1}}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{b}+\mathrm{23}\: \\ $$ Answered by john santu last updated on 28/Jul/20…

lim-t-0-1-t-ln-1-ln-1-t-ln-t-

Question Number 105331 by Ar Brandon last updated on 27/Jul/20 $$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{t}}\mathrm{ln}\left[\mathrm{1}−\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)}{\mathrm{ln}\left(\mathrm{t}\right)}\right] \\ $$ Commented by bubugne last updated on 28/Jul/20 $$ \\ $$$$=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{t}}\mathrm{ln}\left[\frac{\mathrm{ln}\left(\mathrm{t}\right)−\:\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)}{\mathrm{ln}\left(\mathrm{t}\right)}\right]…

lim-x-x-7-x-6-1-1-7-x-5-1-x-9-1-9-

Question Number 170766 by cortano1 last updated on 30/May/22 $$\:\:\:\:\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{7}}]{{x}^{\mathrm{7}} +{x}^{\mathrm{6}} −\mathrm{1}}\:+\sqrt[{\mathrm{9}}]{{x}^{\mathrm{5}} +\mathrm{1}−{x}^{\mathrm{9}} }\:=? \\ $$ Answered by aleks041103 last updated on 30/May/22 $$\sqrt[{\mathrm{7}}]{{x}^{\mathrm{7}}…

Question-170767

Question Number 170767 by 2407 last updated on 30/May/22 Answered by aleks041103 last updated on 30/May/22 $${L}=\underset{{x}\rightarrow\infty} {{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{5}^{{x}} +\mathrm{7}^{{x}} +\mathrm{9}^{{x}} }\right)^{−\sqrt{\frac{\mathrm{1}}{{x}}}} \\ $$$$\Rightarrow{lnL}=\underset{{x}\rightarrow\infty} {{lim}}\frac{{ln}\left(\mathrm{5}^{{x}} +\mathrm{7}^{{x}}…