Question Number 122824 by bemath last updated on 19/Nov/20 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\:=? \\ $$ Commented by bobhans last updated on 20/Nov/20 $$\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}{x}\right)\right)}{\mathrm{2}{x}^{\mathrm{2}} }…
Question Number 57253 by Tawa1 last updated on 01/Apr/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\:\:\:\frac{\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{e}^{−\mathrm{x}} }{\mathrm{x}}\:\:\:\:\:\: \\ $$ Commented by mr W last updated on 01/Apr/19 $$=\frac{\mathrm{2}}{\mathrm{0}}=\infty \\…
Question Number 122730 by bemath last updated on 19/Nov/20 $$\:{Given}\:{f}\left({x}\right)=\mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}}\right)\:{and}\:{g}\left({x}\right)=\mathrm{tan}\:\mathrm{2}{x}. \\ $$$${Find}\:{the}\:{intersect}\:{point}\:{vertical} \\ $$$${asymptote}\:{f}\left({x}\right)\:{and}\:\:{horizontal}\: \\ $$$${asymptote}\:{g}\left({x}\right)\:{for}\:\mathrm{0}\:\leqslant{x}\leqslant\pi. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122729 by bemath last updated on 19/Nov/20 $$\:{Given}\:\underset{{x}\rightarrow{c}} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\mathrm{1}}{{x}}\right)\:=\:{a}\:{and}\: \\ $$$$\:\underset{{x}\rightarrow{c}} {\mathrm{lim}}\left(\:\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{1}}{{x}}\right)−\mathrm{4sin}\:\left(\frac{\mathrm{1}}{{x}}\right)+\mathrm{1}\:\right)=−\mathrm{2} \\ $$$${find}\:{the}\:{value}\:{of}\:{a}. \\ $$ Answered by liberty last updated on…
Question Number 122725 by liberty last updated on 19/Nov/20 $$\:{Find}\:{the}\:{constants}\:{a}\:{and}\:{b}\:{from}\:{the} \\ $$$${condition}\::\: \\ $$$$\left({i}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}+\mathrm{1}}−{ax}−{b}\right)=\mathrm{0} \\ $$$$\left({ii}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}−{ax}−{b}\right)=\mathrm{0} \\ $$ Commented by Dwaipayan…
Question Number 188259 by alcohol last updated on 27/Feb/23 Answered by mr W last updated on 27/Feb/23 $${m}={m}_{\mathrm{0}} {e}^{{kt}} \\ $$$${kv}_{\mathrm{0}} ={g} \\ $$$$\left({a}\right) \\…
Question Number 122721 by bemath last updated on 19/Nov/20 $$\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}+{x}}{\mathrm{2}+{x}}\right)^{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}−{x}}} \:=?\: \\ $$ Answered by Dwaipayan Shikari last updated on 19/Nov/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\frac{\mathrm{1}+{x}}{\mathrm{2}+{x}}\right)^{\frac{\mathrm{1}−\sqrt{{x}}}{\left(\mathrm{1}+\sqrt{{x}}\right)\left(\mathrm{1}−\sqrt{{x}}\right)}} \\…
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Question Number 122624 by Ar Brandon last updated on 18/Nov/20 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{equality}\:: \\ $$$$\mathrm{n}!=\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{k}} \begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}\left(\mathrm{n}−\mathrm{k}\right)^{\mathrm{n}} \\ $$ Answered by mindispower last updated on 18/Nov/20…
Question Number 122623 by Ar Brandon last updated on 18/Nov/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{at}\:\left(\mathrm{0},\:\mathrm{0}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{functions}\:: \\ $$$$\mathrm{1}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\mathrm{2}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:\:\:\:\:\mathrm{3}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}} \\ $$$$\mathrm{4}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:\:\:\:\:\:\mathrm{5}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{3x}^{\mathrm{2}}…