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…
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Question Number 71096 by Omer Alattas last updated on 11/Oct/19 Answered by $@ty@m123 last updated on 11/Oct/19 $${Let}\:{x}=\mathrm{1}+{y} \\ $$$$\underset{{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\:\frac{{y}}{\mathrm{ln}\:\left(\mathrm{1}+{y}\right)} \\ $$$$\:\:\frac{\mathrm{1}}{\underset{{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+{y}\right)}{{y}}}=\mathrm{1} \\…
Question Number 5561 by Rasheed Soomro last updated on 20/May/16 $$\mathrm{A}\:\mathrm{chord}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{that} \\ $$$$\mathrm{divides}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{in}\:\mathrm{1}:\mathrm{2}\:\left(\mathrm{ratio}\right). \\ $$$$\mathrm{In}\:\mathrm{what}\:\mathrm{ratio}\:\mathrm{the}\:\mathrm{chord}\:\mathrm{divides} \\ $$$$\mathrm{the}\:\mathrm{diameter}\:\mathrm{perpendicular}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{chord}? \\ $$ Commented by Rasheed Soomro…
Question Number 5556 by Rasheed Soomro last updated on 20/May/16 $$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{diretly}\: \\ $$$$\mathrm{proportional}\:\mathrm{to}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{diameter}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{proportionality}? \\ $$ Commented by Yozzii last updated on…
Question Number 71091 by Henri Boucatchou last updated on 11/Oct/19 Commented by Prithwish sen last updated on 11/Oct/19 $$\boldsymbol{\mathrm{It}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{as}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\mathrm{1}}\:\boldsymbol{\mathrm{dx}}\:−\int_{\mathrm{0}}…
Question Number 136626 by mnjuly1970 last updated on 24/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……….{nice}\:\:\:\:{calculus}……… \\ $$$$\:\:\:\:{suppose}\:{that}::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\varphi\left({p}\right)=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}\right)}{\left({p}+{x}\right)^{\mathrm{2}} }\:…\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}:: \\ $$$$\:\:\:\:\:\:\:\underset{\mathrm{0}} {\int}^{\:\mathrm{1}} \:\frac{\varphi\left({p}\right)}{\mathrm{1}+{p}}{dp}=?… \\ $$$$\:\:\:\:\:\:…