Question Number 164122 by qaz last updated on 14/Jan/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{k}}=? \\ $$ Answered by mathmax by abdo last updated on 15/Jan/22 $$\mathrm{we}\:\mathrm{know}\:\:\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}}…
Question Number 98539 by Rio Michael last updated on 14/Jun/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{function} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{ln}\:{x}}{{x}−\mathrm{1}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{State}\:\mathrm{the}\:\mathrm{domain}\:{D}_{{f}} \:\mathrm{of}\:{f}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\:{x}}{{x}−\mathrm{1}}.\:\mathrm{State}\:\mathrm{its}\:\mathrm{asymptotes}. \\ $$$$\left(\mathrm{c}\right)\:\mathrm{Draw}\:\mathrm{up}\:\mathrm{a}\:\mathrm{variation}\:\mathrm{table}\:\mathrm{for}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right).\: \\ $$ Answered by…
Question Number 32991 by abdo imad last updated on 09/Apr/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{ln}\left(\mathrm{1}+{x}\right)\:−{x}}{{x}^{\mathrm{2}} }\:. \\ $$ Commented by prof Abdo imad last updated on 09/Apr/18 $${for}\:\mid{x}\mid<\mathrm{1}\:\:\:\left({ln}\left(\mathrm{1}+{x}\right)\right)^{'}…
Question Number 32992 by abdo imad last updated on 09/Apr/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{tan}\left({sinx}\right)\:−{sin}\left({tanx}\right)}{{x}^{\mathrm{2}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98506 by bemath last updated on 14/Jun/20 Commented by john santu last updated on 14/Jun/20 $$\mathrm{set}\:\frac{\mathrm{1}}{{x}}\:=\:{z}\:,\:{z}\rightarrow\mathrm{0} \\ $$$$\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{7}\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{2}{z}^{\mathrm{5}} \right)}{\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\:\mathrm{tan}\:\left(\mathrm{2}{z}^{\mathrm{3}} \right)}\:=\:\mathrm{7}\:\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{z}^{\mathrm{2}}…
Question Number 163966 by bobhans last updated on 12/Jan/22 $$\:\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2tan}\:^{\mathrm{2}} \mathrm{x}+\mathrm{3}}−\sqrt{\mathrm{2tan}\:^{\mathrm{2}} \mathrm{x}+\mathrm{10}}}{\mathrm{cot}\:\mathrm{x}}\:=? \\ $$ Answered by cortano1 last updated on 12/Jan/22 $$\:{set}\:{x}=\frac{\pi}{\mathrm{2}}+{h}\Rightarrow\begin{cases}{\mathrm{tan}\:{x}=−\mathrm{cot}\:{h}}\\{\mathrm{cot}\:{x}=−\mathrm{tan}\:{h}}\end{cases} \\ $$$$\:\underset{{h}\rightarrow\mathrm{0}}…
Question Number 163961 by qaz last updated on 12/Jan/22 $$\underset{\mathrm{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\:\frac{\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}} }{\mathrm{x}−\mathrm{1}}=? \\ $$ Answered by bobhans last updated on 12/Jan/22 $$\:\mathrm{x}−\mathrm{1}=\mathrm{u}\Rightarrow\mathrm{x}=\mathrm{u}+\mathrm{1} \\…
Question Number 163960 by bobhans last updated on 12/Jan/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}+\mathrm{7cot}\:^{\mathrm{2}} \mathrm{x}}−\sqrt{\mathrm{7}+\mathrm{7cot}\:^{\mathrm{2}} \mathrm{x}}}{\mathrm{tan}\:\mathrm{x}}\:=? \\ $$ Answered by cortano1 last updated on 12/Jan/22 Terms of Service…
Question Number 163959 by mathlove last updated on 12/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163938 by cortano1 last updated on 12/Jan/22 $$\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(−\mathrm{3}{x}\right)−\mathrm{cos}\:\left(\mathrm{3}{x}\right)}{\mathrm{sin}\:^{\mathrm{2}} \left({x}\sqrt{\mathrm{5}}\:\right)}=? \\ $$ Answered by 770551415 last updated on 12/Jan/22 $$\boldsymbol{{Solution}}:\:{cos}\:{y}\:{is}\:{even}\: \\ $$$$\:\:{cos}\left(−\mathrm{3}{x}\right)={cos}\left(\mathrm{3}{x}\right)\: \\…