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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?

Question Number 11456 Answers: 2 Comments: 3

sin x − cos x = a, (π/4) ≤ x ≤ (π/2) Which statement is correct? (1) sin^2 x − cos^2 x = −(1/2)(√(3 + 2a^2 − a^4 )) (2) sin^4 x + cos^4 x = (1/8)(−3a^4 + 6a^2 + 5) (3) sin 2x = ((1 − a^2 )/2) (4) tan^2 x + cot^2 x = ((−3a^4 − 2a^2 + 8a + 13 )/(2(a^4 + 2a^2 + 1)))

$$\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\:=\:{a},\:\:\frac{\pi}{\mathrm{4}}\:\leqslant\:{x}\:\leqslant\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{Which}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{sin}^{\mathrm{2}} \:{x}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}\:=\:−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{3}\:+\:\mathrm{2}{a}^{\mathrm{2}} \:−\:{a}^{\mathrm{4}} } \\ $$$$\left(\mathrm{2}\right)\:\mathrm{sin}^{\mathrm{4}} \:{x}\:+\:\mathrm{cos}^{\mathrm{4}} \:{x}\:=\:\frac{\mathrm{1}}{\mathrm{8}}\left(−\mathrm{3}{a}^{\mathrm{4}} \:+\:\mathrm{6}{a}^{\mathrm{2}} \:+\:\mathrm{5}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\frac{\mathrm{1}\:−\:{a}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{tan}^{\mathrm{2}} \:{x}\:+\:\mathrm{cot}^{\mathrm{2}} \:{x}\:=\:\frac{−\mathrm{3}{a}^{\mathrm{4}} \:−\:\mathrm{2}{a}^{\mathrm{2}} \:+\:\mathrm{8}{a}\:+\:\mathrm{13}\:}{\mathrm{2}\left({a}^{\mathrm{4}} \:+\:\mathrm{2}{a}^{\mathrm{2}} \:+\:\mathrm{1}\right)} \\ $$

Question Number 11453 Answers: 0 Comments: 0

$$\: \\ $$

Question Number 11444 Answers: 2 Comments: 0

If lim_(x→0) (((√(px + q)) − 2)/x) = 1 What is the value of p + q ?

$$\mathrm{If}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{px}\:+\:{q}}\:−\:\mathrm{2}}{{x}}\:=\:\mathrm{1} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{p}\:+\:{q}\:? \\ $$

Question Number 11436 Answers: 0 Comments: 1

∫_0 ^(𝛑/4) sinx×cos^7 x dx. solves...

$$ \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\boldsymbol{\pi}}{\mathrm{4}}} {\int}}\boldsymbol{\mathrm{sinx}}×\boldsymbol{\mathrm{cos}}^{\mathrm{7}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}. \\ $$$$\boldsymbol{\mathrm{solves}}... \\ $$

Question Number 11433 Answers: 1 Comments: 5

for r=(1/θ), show that the arc length between θ=3π^(−1) and θ=nπ^(−1) (where n>3) is aproxiately equal to the length of the line y=3π^(−1) between the same bounds. Or show otherwise.

$$\mathrm{for}\:{r}=\frac{\mathrm{1}}{\theta},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{between} \\ $$$$\theta=\mathrm{3}\pi^{−\mathrm{1}} \:\:\mathrm{and}\:\theta={n}\pi^{−\mathrm{1}} \:\:\:\left(\mathrm{where}\:\:{n}>\mathrm{3}\right)\:\:\mathrm{is}\:\mathrm{aproxiately} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:{y}=\mathrm{3}\pi^{−\mathrm{1}} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{same}\:\mathrm{bounds}.\:\mathrm{Or}\:\mathrm{show}\:\mathrm{otherwise}. \\ $$$$ \\ $$

Question Number 11429 Answers: 1 Comments: 0

∫_0 ^3 ((2x+3)/(2x+1))dx=𝛂+ln7. 𝛂=? please......

$$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{3}}{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1}}\boldsymbol{\mathrm{dx}}=\boldsymbol{\alpha}+\boldsymbol{\mathrm{ln}}\mathrm{7}. \\ $$$$\boldsymbol{\alpha}=? \\ $$$$\boldsymbol{\mathrm{please}}...... \\ $$

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