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)}} \\…
Question Number 188251 by Rupesh123 last updated on 27/Feb/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
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 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{at}\:\left(\mathrm{0},\:\mathrm{0}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{functions}\:: \\ $$$$\mathrm{1}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\mathrm{2}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:\:\:\:\:\mathrm{3}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}} \\ $$$$\mathrm{4}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:\:\:\:\:\:\mathrm{5}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{3x}^{\mathrm{2}}…
Question Number 57073 by gunawan last updated on 31/Mar/19 $${f}\left({x}\right)={A} \\ $$$${f}\::\:\left[\mathrm{0},\:\infty\right)\: \\ $$$${g}\::\:\left[\mathrm{1},\:\mathrm{0}\right] \\ $$$${g}\left({x}\right)={B} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{n}}\int_{\mathrm{0}} ^{{n}} {f}\left({x}\right){g}\left(\frac{{x}}{{n}}\right){dx}=… \\ $$ Commented by…
Question Number 122550 by liberty last updated on 18/Nov/20 $$\:\:\underset{{x}\rightarrow\mathrm{1}/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{2x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}}{\mathrm{tan}\:\left(\pi\mathrm{x}\right)}\:? \\ $$ Answered by bramlexs22 last updated on 18/Nov/20 $$\:\:\underset{{x}\rightarrow\mathrm{1}/\mathrm{2}} {\mathrm{lim}}\:\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)}{\mathrm{tan}\:\left(\pi{x}\right)}\:= \\ $$$$\:\frac{\mathrm{3}}{\mathrm{2}}×\:\underset{{x}\rightarrow\mathrm{1}/\mathrm{2}}…
Question Number 122548 by bramlexs22 last updated on 18/Nov/20 $$\:\:\underset{{x}\rightarrow\mathrm{1}/\mathrm{2}} {\mathrm{lim}}\:\left(\frac{\mathrm{cot}\:\left(\pi{x}\right)}{\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{1}}\right)=?\: \\ $$ Answered by liberty last updated on 18/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{1}/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{cot}\:\left(\pi\mathrm{x}\right)}{\left(\mathrm{2x}−\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)}\:=\:\underset{{x}\rightarrow\mathrm{1}/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{x}+\mathrm{1}}.\underset{\left(\frac{\mathrm{2x}−\mathrm{1}}{\mathrm{2}}\right)\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cot}\:\left(\pi\mathrm{x}\right)}{\left(\mathrm{2x}−\mathrm{1}\right)}…