Question Number 68203 by peter frank last updated on 07/Sep/19 Commented by Cmr 237 last updated on 07/Sep/19 $$\eth\mathrm{f}=\frac{\eth\mathrm{f}}{\eth\mathrm{x}}+\frac{\eth\mathrm{f}}{\eth\mathrm{y}}+\frac{\eth\mathrm{f}}{\eth\mathrm{z}} \\ $$$$\:\:\:\:=\mathrm{2xy}+\mathrm{cosh}\left(\mathrm{yz}\right)+\mathrm{x}^{\mathrm{2}} +\mathrm{xzsinh}\left(\mathrm{yz}\right)+\mathrm{xysinh}\left(\mathrm{yz}\right) \\ $$ Commented…
Question Number 68191 by peter frank last updated on 06/Sep/19 Answered by mind is power last updated on 06/Sep/19 $${sin}\left({a}−{b}\right)={sin}\left({a}\right){cos}\left({b}\right)−{cos}\left({a}\right){sin}\left({b}\right) \\ $$$$\frac{{sin}\left({a}−{b}\right)}{{cos}\left({a}\right){cos}\left({b}\right)}={tg}\left({a}\right)−{tg}\left({b}\right) \\ $$$$\Rightarrow\frac{{sin}\left({a}−{b}\right)}{{cos}\left({a}\right){cos}\left({b}\right)}={tg}\left({b}\right)\left({k}−\mathrm{1}\right) \\…
Question Number 68189 by peter frank last updated on 06/Sep/19 Commented by peter frank last updated on 06/Sep/19 $${Qn}\:\mathrm{9},\:\:\mathrm{10} \\ $$ Commented by mind is…
Question Number 2589 by Filup last updated on 23/Nov/15 $${f}_{{n}} =\frac{\mathrm{1}}{{n}}\left({n}+{f}_{{n}−\mathrm{1}} \right) \\ $$$${f}_{\mathrm{1}} =\mathrm{1} \\ $$$$ \\ $$$$\mathrm{Evaluate}: \\ $$$${S}=\underset{{i}=\mathrm{1}} {\overset{{m}} {\sum}}{f}_{{i}} \\ $$…
Question Number 2400 by Filup last updated on 19/Nov/15 $$\mathrm{According}\:\mathrm{to}\:\mathrm{Wikipedia}\:\mathrm{and}\:\mathrm{WolframAlpha}, \\ $$$$\mathrm{the}\:\mathrm{sign}\:\mathrm{function},\:\mathrm{sgn}\left({x}\right),\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as}: \\ $$$$ \\ $$$$\mathrm{sgn}\left({x}\right)\equiv\frac{{x}}{\mid{x}\mid}=\frac{\mid{x}\mid}{{x}}\:\:\:\mathrm{for}\:{x}\neq\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{satisfies}: \\ $$$$\mathrm{sgn}\left({x}\right)=\sqrt{{x}}\sqrt{\frac{\mathrm{1}}{{x}}} \\ $$$$\boldsymbol{{but}} \\ $$$$\mathrm{sgn}\left(\mathrm{0}\right)=\mathrm{0} \\…
Question Number 67871 by rrebo5637@gmail.com last updated on 01/Sep/19 $$\mathrm{8}=\mathrm{4x} \\ $$$$\mathrm{x}=? \\ $$ Commented by Prithwish sen last updated on 01/Sep/19 $$\mathrm{2} \\ $$…
Question Number 2275 by Filup last updated on 13/Nov/15 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{way}\:\mathrm{to}\:\mathrm{evaluate}\:\mathrm{the}\:\mathrm{following}: \\ $$$$ \\ $$$${S}=\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+…}}}} \\ $$ Answered by Rasheed Soomro last updated on 13/Nov/15 $${S}=\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+…}}}}…
Question Number 2181 by Filup last updated on 07/Nov/15 $$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{series}? \\ $$$$\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{i}} \frac{\mathrm{1}}{\mathrm{2}\left({i}+\mathrm{1}\right)} \\ $$ Answered by prakash jain last updated on 08/Nov/15…
Question Number 133146 by shaker last updated on 19/Feb/21 Commented by Dwaipayan Shikari last updated on 19/Feb/21 $$\frac{\mathrm{1}−{a}^{{n}+\mathrm{1}} }{\mathrm{1}−{a}}\:\:\:\: \\ $$ Answered by mathmax by…
Question Number 67481 by Mohamed Amine Bouguezzoul last updated on 27/Aug/19 $${p}\:{is}\:{a}\:{prime}\:{number}\:{such}\:{that}\:\left(\mathrm{1}+{p}\right)^{{p}} \equiv\mathrm{2}\left[\mathrm{7}\right] \\ $$$${find}\:{all}\:{k}\:{such}\:{that}\:{p}\equiv{k}\left[\mathrm{42}\right] \\ $$ Commented by Rasheed.Sindhi last updated on 30/Aug/19 $$\boldsymbol{{Some}}\:{values}\:{of}\:{k}…