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AllQuestion and Answers: Page 1957

Question Number 11581 Answers: 2 Comments: 0

cAn you prove the chAin role??

$${cAn}\:{you}\:{prove}\:{the}\:{chAin}\:{role}?? \\ $$

Question Number 11580 Answers: 1 Comments: 0

why (dy/dx)=(dy/du).(du/dx)

$${why}\:\frac{{dy}}{{dx}}=\frac{{dy}}{{du}}.\frac{{du}}{{dx}} \\ $$

Question Number 11571 Answers: 2 Comments: 0

why ((d[f{g(x)}])/dx)=((df[{g(x)}])/(dg(x))).((dg(x))/dx)?

$${why}\:\:\:\frac{{d}\left[{f}\left\{{g}\left({x}\right)\right\}\right]}{{dx}}=\frac{{df}\left[\left\{{g}\left({x}\right)\right\}\right]}{{dg}\left({x}\right)}.\frac{{dg}\left({x}\right)}{{dx}}? \\ $$

Question Number 11567 Answers: 1 Comments: 0

why lim_(x→0) ((f(x))/(g(x)))=lim_(x→0) ((f′(x))/(g′(x)))

$${why}\:\:\:\:\:\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}={li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{f}'\left({x}\right)}{{g}'\left({x}\right)} \\ $$

Question Number 11565 Answers: 1 Comments: 0

if (dy/dx)=p ,then why dy=pdx?

$${if}\:\frac{{dy}}{{dx}}={p}\:\:,{then}\:{why}\:{dy}={pdx}? \\ $$

Question Number 11563 Answers: 1 Comments: 2

if f(x)=g(y) then why (d/dx)(f(x))=(d/dy)(g(y))?

$${if}\:\:{f}\left({x}\right)={g}\left({y}\right) \\ $$$${then}\:{why}\:\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\frac{{d}}{{dy}}\left({g}\left({y}\right)\right)? \\ $$

Question Number 11552 Answers: 1 Comments: 0

find (d/dx)(y) where y= ^(√x) (√(√x))

$${find}\:\frac{{d}}{{dx}}\left({y}\right)\:{where}\:\:{y}=\overset{\sqrt{{x}}} {\:}\sqrt{\sqrt{{x}}} \\ $$$$ \\ $$

Question Number 11549 Answers: 1 Comments: 0

proof lim h→0^(((x^h −1)/h)=ln(x))

$$\:\:\:\: \\ $$$${proof} \\ $$$${lim} \\ $$$${h}\rightarrow\mathrm{0}^{\frac{{x}^{{h}} −\mathrm{1}}{{h}}={ln}\left({x}\right)} \\ $$

Question Number 11548 Answers: 1 Comments: 0

find (d/dx)(2^x )

$$ \\ $$$${find}\:\frac{{d}}{{dx}}\left(\mathrm{2}^{{x}} \right) \\ $$

Question Number 11547 Answers: 2 Comments: 0

(d/dx)(x^x )=?[please give the answer with proof]

$$\:\:\:\:\:\:\:\:\:\:\frac{{d}}{{dx}}\left({x}^{{x}} \right)=?\left[{please}\:{give}\:{the}\:{answer}\:{with}\:{proof}\right] \\ $$

Question Number 11546 Answers: 2 Comments: 0

f(x)=^x (√x) find (d/dx)(f(x)) and for what x ,we will get the maximum of the function..?

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:{f}\left({x}\right)=^{{x}} \sqrt{{x}}\:{find}\:\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{and}\:{for}\:{what}\:{x}\:,{we}\:{will}\:{get}\:{the}\: \\ $$$$\:{maximum}\:{of}\:{the}\:{function}..? \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\: \\ $$

Question Number 11545 Answers: 2 Comments: 0

find(dy/dx) if x^x y^y =1

$${find}\frac{{dy}}{{dx}}\:{if}\:{x}^{{x}} {y}^{{y}} =\mathrm{1} \\ $$

Question Number 11544 Answers: 1 Comments: 0

Evaluate ∫x^3 e^(2x) dx

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:{Evaluate}\:\int{x}^{\mathrm{3}} {e}^{\mathrm{2}{x}} {dx} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 11543 Answers: 2 Comments: 0

solve for x and y in this equation x^x +y^y =31 x+y=5

$${solve}\:{for}\:{x}\:{and}\:{y}\:{in}\:{this}\:{equation} \\ $$$${x}^{{x}} +{y}^{{y}} =\mathrm{31} \\ $$$${x}+{y}=\mathrm{5} \\ $$

Question Number 11540 Answers: 1 Comments: 0

Question Number 11536 Answers: 2 Comments: 0

Question Number 11515 Answers: 2 Comments: 0

(((4+x)/x))^(1/5) −(((4−6x)/x))^(1/5) =1. x_1 +x_2 =?

$$\sqrt[{\mathrm{5}}]{\frac{\mathrm{4}+\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}−\sqrt[{\mathrm{5}}]{\frac{\mathrm{4}−\mathrm{6}\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}=\mathrm{1}. \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{1}} +\boldsymbol{\mathrm{x}}_{\mathrm{2}} =? \\ $$

Question Number 11517 Answers: 2 Comments: 0

f : R → R If x^2 f(x) + f(1−x) = 2x − x^4 Determine f(x)

$${f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R} \\ $$$$\mathrm{If}\:\:{x}^{\mathrm{2}} {f}\left({x}\right)\:+\:{f}\left(\mathrm{1}−{x}\right)\:=\:\mathrm{2}{x}\:−\:{x}^{\mathrm{4}} \\ $$$$\mathrm{Determine}\:{f}\left({x}\right) \\ $$

Question Number 11501 Answers: 3 Comments: 1

(4x^2 −7x−5)(5x^2 +13x+3)(3x−x^2 −8)=0. find all the multiples of the real roots of the equation.

Question Number 11500 Answers: 2 Comments: 0

(x^2 +x−4)(x^2 +x+4)=9 find the equation has multiple roots.

$$\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}−\mathrm{4}\right)\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\mathrm{4}\right)=\mathrm{9} \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}\:\:\boldsymbol{\mathrm{has}}\:\:\boldsymbol{\mathrm{multiple}}\:\:\boldsymbol{\mathrm{roots}}. \\ $$

Question Number 11477 Answers: 2 Comments: 0

((a^8 +a^4 +1)/(a^6 +1)). solves....

$$\frac{\boldsymbol{\mathrm{a}}^{\mathrm{8}} +\boldsymbol{\mathrm{a}}^{\mathrm{4}} +\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{6}} +\mathrm{1}}. \\ $$$$\boldsymbol{\mathrm{solves}}.... \\ $$

Question Number 11476 Answers: 1 Comments: 0

Question Number 11475 Answers: 2 Comments: 0

Question Number 11474 Answers: 1 Comments: 0

Question Number 11473 Answers: 1 Comments: 1

Show that the graph of y = x^3 + 2x^2 + x + 1 , between x = − 1 and x = 2 lies entirely above the x − axis

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\:,\:\mathrm{between}\:\mathrm{x}\:=\:−\:\mathrm{1}\:\mathrm{and}\:\mathrm{x}\:=\:\mathrm{2} \\ $$$$\mathrm{lies}\:\mathrm{entirely}\:\mathrm{above}\:\mathrm{the}\:\mathrm{x}\:−\:\mathrm{axis} \\ $$

Question Number 11459 Answers: 2 Comments: 0

If ((4x^2 −4xy+3y^2 )/(2y^2 +2xy−5x^2 ))=1 if the ((x+y)/(x−y)) what is th value?

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