Question Number 136651 by mhabs last updated on 24/Mar/21 Answered by Ñï= last updated on 24/Mar/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{1}}{\mathrm{1}+\left({a}\mathrm{tan}\:{x}\right)^{\mathrm{2}} }{dx}\overset{{t}=\mathrm{tan}\:{x}} {=}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\mathrm{1}+{a}^{\mathrm{2}} {t}^{\mathrm{2}} }\centerdot\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 136645 by Dwaipayan Shikari last updated on 24/Mar/21 $$\frac{\mathrm{1}}{\mathrm{1}+\frac{\eta^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\eta+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\eta+\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\eta+\mathrm{3}\right)^{\mathrm{2}} }{\mathrm{1}+..}\:\:}}}}=\frac{\mathrm{1}}{\mathrm{2}}\psi\left(\frac{\eta+\mathrm{2}}{\mathrm{2}}\right)−\frac{\mathrm{1}}{\mathrm{2}}\psi\left(\frac{\eta+\mathrm{1}}{\mathrm{2}}\right)\:\:\left(\eta>\mathrm{0}\right) \\ $$$${Or}\:\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\boldsymbol{\mathrm{K}}}}\left(\eta+{r}\right)^{\mathrm{2}} =\frac{\mathrm{2}}{\psi\left(\frac{\eta}{\mathrm{2}}+\mathrm{1}\right)−\psi\left(\frac{\eta+\mathrm{1}}{\mathrm{2}}\right)} \\ $$ Terms of Service…
Question Number 136644 by mnjuly1970 last updated on 24/Mar/21 $$ \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{log}\left({ax}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:\:{f}\:'\left({a}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}}…
Question Number 136640 by jahar last updated on 24/Mar/21 $${if}\:\frac{{x}+{y}}{\mathrm{3}{a}−{b}}=\:\frac{{y}+{z}}{\mathrm{3}{b}−{c}}=\frac{{z}+{x}}{\mathrm{3}{c}−{a}}\:{then}\: \\ $$$${prove}\:{that}\:,\frac{{x}+{y}+{z}}{{a}+{b}+{c}}\:=\:\:\:\frac{{ax}+{by}+{cz}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136643 by Ñï= last updated on 24/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{sin}^{−\mathrm{1}} \sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}+{x}^{\mathrm{2}} }}{dx}=\frac{\pi}{\mathrm{4}}{ln}\mathrm{3} \\ $$ Answered by Ñï= last updated on 24/Mar/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 5569 by Rasheed Soomro last updated on 20/May/16 $$\mathrm{The}\:\mathrm{result}\:“\mathrm{log}\:\mathrm{xy}=\mathrm{log}\:\mathrm{x}+\mathrm{log}\:\mathrm{y}''\:\mathrm{is}\:\mathrm{not} \\ $$$$\mathrm{always}\:\mathrm{true}!\:\mathrm{Give}\:\mathrm{a}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{result}\:\mathrm{will}\:\mathrm{not}\:\mathrm{hold}. \\ $$ Commented by Yozzii last updated on 20/May/16 $$\left({x},{y}\right)=\left(−\mathrm{1},\mathrm{2}\right)…
Question Number 5568 by Rasheed Soomro last updated on 20/May/16 $$\mathrm{Solve}\:\mathrm{without}\:\mathrm{using}\:\mathrm{calculator} \\ $$$$\mathrm{4}^{\mathrm{x}} −\mathrm{3}^{\mathrm{x}+\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{3}^{\mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}} −\mathrm{2}^{\mathrm{2x}−\mathrm{1}} \\ $$ Answered by Yozzii last updated on 20/May/16…
Question Number 136636 by Raxreedoroid last updated on 24/Mar/21 $${b}={a}+{c} \\ $$$${y}={x}+{c} \\ $$$${x}={a}+{z} \\ $$$${y}={b}+{z} \\ $$$${x}=?,{y}=?,{z}=? \\ $$ Commented by mr W last…
Question Number 136635 by mohammad17 last updated on 24/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 71096 by Omer Alattas last updated on 11/Oct/19 Answered by $@ty@m123 last updated on 11/Oct/19 $${Let}\:{x}=\mathrm{1}+{y} \\ $$$$\underset{{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\:\frac{{y}}{\mathrm{ln}\:\left(\mathrm{1}+{y}\right)} \\ $$$$\:\:\frac{\mathrm{1}}{\underset{{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+{y}\right)}{{y}}}=\mathrm{1} \\…