Question Number 188017 by Rupesh123 last updated on 24/Feb/23 Answered by aleks041103 last updated on 24/Feb/23 $${f}\left({x},{y}\right)={ln}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)=\mathrm{2}{ln}\left({r}\right) \\ $$$${r}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$$$\Rightarrow{f}\left({x},{y}\right)={f}\left({r}\right)…
Question Number 122434 by benjo_mathlover last updated on 17/Nov/20 $$\:{If}\:{f}\left({x}\right)\:=\:\int_{{a}} ^{\:\left(\underset{{a}} {\overset{{x}^{\mathrm{3}} } {\int}}\:\frac{{dt}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} {t}}\:\right)} \left(\frac{{dt}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} {t}}\right) \\ $$$${then}\:{f}\:'\left({x}\right)\:? \\ $$ Answered by liberty last…
Question Number 122393 by benjo_mathlover last updated on 16/Nov/20 $$\:\:{f}\left({x}\right)\:=\:{x}\:\mid{x}−\mathrm{1}\mid\:\Rightarrow{f}\:'\left(\mathrm{1}\right)=? \\ $$ Answered by MJS_new last updated on 16/Nov/20 $$\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$ Answered by Bird…
Question Number 122348 by liberty last updated on 16/Nov/20 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{derivative}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{implicit}\:\mathrm{function}\:\underset{\pi/\mathrm{2}} {\overset{\mathrm{x}} {\int}}\sqrt{\mathrm{3}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{z}}\:\mathrm{dz}\:+\:\underset{\mathrm{0}} {\overset{\mathrm{y}} {\int}}\:\mathrm{cos}\:\mathrm{t}\:\mathrm{dt}.\: \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 56749 by pete last updated on 22/Mar/19 $$\mathrm{The}\:\mathrm{curve}\:\mathrm{y}=\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}\:\mathrm{crosses}\:\mathrm{the} \\ $$$$\mathrm{y}−\mathrm{axis}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{0},\mathrm{3}\right)\:\mathrm{and}\:\mathrm{has} \\ $$$$\mathrm{stationary}\:\mathrm{point}\:\mathrm{at}\:\left(\mathrm{1},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{values}\:\mathrm{of}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}. \\ $$ Answered by ajfour last updated on…
Question Number 56738 by pieroo last updated on 22/Mar/19 $$\mathrm{The}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\mathrm{x}^{\mathrm{3}} +\mathrm{bx},\:\mathrm{where} \\ $$$$\mathrm{b}\:\mathrm{is}\:\mathrm{constant},\:\mathrm{at}\:\mathrm{x}=\mathrm{1}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the} \\ $$$$\mathrm{points}\:\mathrm{A}\left(−\mathrm{1},\mathrm{6}\right)\:\mathrm{and}\:\left(\mathrm{2},−\mathrm{15}\right).\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{b}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 122264 by mnjuly1970 last updated on 15/Nov/20 Commented by mr W last updated on 15/Nov/20 $$\left(\mathrm{1}+{x}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(_{{k}} ^{{n}} \right){x}^{{k}} \\ $$$$\left(\mathrm{1}−\mathrm{1}\right)^{{n}}…
Question Number 122185 by mnjuly1970 last updated on 14/Nov/20 $$\:\:\:\:\:\:…\:{challanging}\:\:{math}… \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \zeta\left({n}\right)}{\mathrm{2}^{{n}−\mathrm{1}} {n}}\overset{???} {=}\gamma\:+{ln}\left(\frac{\pi}{\mathrm{4}}\right)\: \\ $$$$\:\:{hint}\:::\:\zeta\left({s}\right)=\frac{\mathrm{1}}{\Gamma\left({s}\right)}\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{{s}−\mathrm{1}} }{{e}^{{x}} −\mathrm{1}}{dx}…