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Category: Differentiation

Find-the-derivative-dy-dx-of-the-following-implicit-function-pi-2-x-3-2sin-2-z-dz-0-y-cos-t-dt-

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:…

The-curve-y-ax-2-bx-c-crosses-the-y-axis-at-the-point-0-3-and-has-stationary-point-at-1-2-Find-the-values-of-a-b-and-c-

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…

The-tangent-to-the-curve-y-x-3-bx-where-b-is-constant-at-x-1-passes-through-the-points-A-1-6-and-2-15-Find-the-value-of-b-

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…

challanging-math-prove-that-n-2-1-n-n-2-n-1-n-ln-pi-4-hint-s-1-s-0-x-s-1-e-x-1-dx-m-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}…

Find-concave-up-and-concove-down-of-function-f-x-x-2-x-3-

Question Number 121956 by bemath last updated on 13/Nov/20 $${Find}\:{concave}\:{up}\:{and}\:{concove}\:{down} \\ $$$${of}\:{function}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:\mid{x}−\mathrm{3}\mid\: \\ $$ Answered by MJS_new last updated on 13/Nov/20 $${f}\left({x}\right)=\begin{cases}{\mathrm{3}{x}^{\mathrm{2}} −{x}^{\mathrm{3}} ;\:{x}<\mathrm{3}}\\{{x}^{\mathrm{3}}…