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Category: Limits

lim-x-0-tan-cos-2x-1-2x-2-

Question Number 105614 by bemath last updated on 30/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}\:\left(\mathrm{cos}\:\mathrm{2}{x}−\mathrm{1}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\:? \\ $$ Commented by PRITHWISH SEN 2 last updated on 30/Jul/20 $$\mathrm{let}\:\mathrm{cos2x}−\mathrm{1}=\mathrm{t}\Rightarrow\mathrm{x}\rightarrow\mathrm{0}\:\mathrm{then}\:\mathrm{t}\rightarrow\mathrm{0} \\…

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…