Question Number 77309 by TawaTawa last updated on 05/Jan/20 Commented by mr W last updated on 05/Jan/20 $$=\infty \\ $$ Commented by mathmax by abdo…
Question Number 77234 by TawaTawa last updated on 04/Jan/20 Answered by mr W last updated on 04/Jan/20 $$=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{4}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{4}}×\frac{\mathrm{1}}{\mathrm{5}}} …{dx} \\…
Question Number 142745 by iloveisrael last updated on 05/Jun/21 Commented by MJS_new last updated on 05/Jun/21 $$\mathrm{vr}×\mathrm{th7gr}\:\mathrm{bl}\theta\mathrm{p}\:\mathrm{njk}\Pi\mathrm{y}\notin\mathrm{m}\:\mathrm{trf}\digamma\mathrm{sh5jk}\:\left[\spadesuit>{bkl}\right. \\ $$ Commented by iloveisrael last updated on…
Question Number 142721 by mathlove last updated on 04/Jun/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}}{\:\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}}=? \\ $$ Answered by Ar Brandon last updated on 04/Jun/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}}{\:\sqrt{\mathrm{1}−\mathrm{cosx}}}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}}{\:\sqrt{\mathrm{1}−\left(\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}\right)}}=\underset{\mathrm{x}\rightarrow\mathrm{0}}…
Question Number 77182 by jagoll last updated on 04/Jan/20 $$ \\ $$$$ \\ $$$$\mathrm{evaluate}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\underset{\mathrm{a}} {\overset{\mathrm{x}} {\int}}\left(\frac{\mathrm{cos}\:\mathrm{t}}{\mathrm{t}}\right)\mathrm{dt}}{\mathrm{x}}\:. \\ $$ Commented by mathmax by abdo last…
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Question Number 11549 by Nayon last updated on 28/Mar/17 $$\:\:\:\: \\ $$$${proof} \\ $$$${lim} \\ $$$${h}\rightarrow\mathrm{0}^{\frac{{x}^{{h}} −\mathrm{1}}{{h}}={ln}\left({x}\right)} \\ $$ Answered by mrW1 last updated on…
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Question Number 11444 by Joel576 last updated on 26/Mar/17 $$\mathrm{If}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{px}\:+\:{q}}\:−\:\mathrm{2}}{{x}}\:=\:\mathrm{1} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{p}\:+\:{q}\:? \\ $$ Answered by ajfour last updated on 26/Mar/17 $$\mathrm{then}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{q}}\left(\mathrm{1}+\mathrm{px}/\mathrm{q}\right)^{\mathrm{1}/\mathrm{2}} \:−\mathrm{2}}{\mathrm{x}}\:=\mathrm{1}…