Question Number 17019 by tawa tawa last updated on 29/Jun/17 $$\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{3}} {\sum}}\:\mathrm{2r}\:−\:\mathrm{1}\:\:=\:\:? \\ $$ Answered by arnabpapu550@gmail.com last updated on 29/Jun/17 $$=\left(\mathrm{2}×\mathrm{1}−\mathrm{1}\right)+\left(\mathrm{2}×\mathrm{2}−\mathrm{1}\right)+\left(\mathrm{2}×\mathrm{3}−\mathrm{1}\right) \\ $$$$=\mathrm{1}+\mathrm{3}+\mathrm{5}=\mathrm{9}…
Question Number 17018 by tawa tawa last updated on 29/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}:\:\:\:\mathrm{55}\:+\:\mathrm{63}\:\sqrt{\mathrm{2}} \\ $$ Commented by prakash jain last updated on 29/Jun/17 $$\left({a}+{b}\sqrt{\mathrm{2}}\right)^{\mathrm{3}} =\mathrm{55}+\mathrm{63}\sqrt{\mathrm{2}} \\ $$$${a}^{\mathrm{3}}…
Question Number 17017 by Mr easymsn last updated on 29/Jun/17 $${solve}\:{the}\:{simultaenous}\:{equation} \\ $$$$\:{x}+{y}=\mathrm{3} \\ $$$$\:\frac{\mathrm{2}^{{x}} }{{x}}=\frac{\mathrm{2}^{{y}} }{{y}} \\ $$$$\:{find}\:{xand}\:{y}.{show}\:{ur}\:{workings}…. \\ $$ Answered by mrW1 last…
Question Number 148090 by mathdanisur last updated on 25/Jul/21 Commented by Rasheed.Sindhi last updated on 25/Jul/21 $$\angle{B}=\mathrm{75}°×\mathrm{2}=\mathrm{150}° \\ $$ Commented by mathdanisur last updated on…
Question Number 82546 by M±th+et£s last updated on 22/Feb/20 $${show}\:{that}\: \\ $$$${if}\:{f}\left({x}\right)={a}^{{x}} \\ $$$$ \\ $$$${show}\:{that}\:{f}\:'\left({x}\right)={a}^{{x}} \:{ln}\left({a}\right) \\ $$$$ \\ $$$${by}\:{using}\:\underset{{h}\rightarrow\mathrm{0}} {{lim}}\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}} \\ $$ Commented…
Question Number 17011 by arnabpapu550@gmail.com last updated on 29/Jun/17 $$\int_{\mathrm{0}} ^{\:\mathrm{a}} \mathrm{x}\sqrt{\frac{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} }}\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 29/Jun/17…
Question Number 17010 by arnabpapu550@gmail.com last updated on 29/Jun/17 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{x}\right)^{\mathrm{2}} \mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 29/Jun/17 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 17009 by arnabpapu550@gmail.com last updated on 29/Jun/17 $$\int_{\mathrm{0}} ^{\:\mathrm{a}} \:\:\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Commented by prakash jain last updated on 29/Jun/17…
Question Number 148082 by tabata last updated on 25/Jul/21 Commented by tabata last updated on 25/Jul/21 $${help}\:{me}\:{msr}\:{olaf} \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 17008 by arnabpapu550@gmail.com last updated on 29/Jun/17 $$\int_{\frac{\mathrm{1}\:}{\Pi}} ^{\frac{\mathrm{2}}{\Pi}} \:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\mathrm{sin}\frac{\mathrm{1}}{\mathrm{x}}\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 29/Jun/17 $${t}=\frac{\mathrm{1}}{{x}}\Rightarrow{dt}=\frac{−{dx}}{{x}^{\mathrm{2}} } \\…