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AllQuestion and Answers: Page 319

Question Number 188082 Answers: 1 Comments: 0

P(x) is a polynomial If P(x^2 + 1) = 6x^4 − x^2 + 5 Find P(x^2 − 1) = ?

$$\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial} \\ $$$$\mathrm{If}\:\:\:\mathrm{P}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:=\:\mathrm{6x}^{\mathrm{4}} \:−\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{5} \\ $$$$\mathrm{Find}\:\:\:\mathrm{P}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{1}\right)\:=\:? \\ $$

Question Number 188079 Answers: 0 Comments: 2

Question Number 188078 Answers: 2 Comments: 0

Question Number 188073 Answers: 2 Comments: 0

If x = (√((1 + (√5))/( (√5) − 1))) find 5x^2 −5x−1=?

$$\mathrm{If}\:\:\:\mathrm{x}\:=\:\sqrt{\frac{\mathrm{1}\:+\:\sqrt{\mathrm{5}}}{\:\sqrt{\mathrm{5}}\:−\:\mathrm{1}}}\:\:\:\:\:\mathrm{find}\:\:\:\:\mathrm{5x}^{\mathrm{2}} −\mathrm{5x}−\mathrm{1}=? \\ $$

Question Number 188072 Answers: 0 Comments: 0

If x_1 =−1 and x_(n+1) = (1 + (2/n))x_n + (4/n) Find x_(2023) = ?

$$\mathrm{If}\:\:\:\mathrm{x}_{\mathrm{1}} =−\mathrm{1}\:\:\:\mathrm{and}\:\:\:\mathrm{x}_{\boldsymbol{\mathrm{n}}+\mathrm{1}} =\:\left(\mathrm{1}\:+\:\frac{\mathrm{2}}{\mathrm{n}}\right)\mathrm{x}_{\boldsymbol{\mathrm{n}}} +\:\frac{\mathrm{4}}{\mathrm{n}} \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{x}_{\mathrm{2023}} \:=\:? \\ $$

Question Number 188071 Answers: 0 Comments: 1

If ((sin^4 x)/5) + ((cos^4 x)/7) = (1/(12)) Find ((sin^2 2x)/5) + ((cos^2 2x)/7) = ?

$$\mathrm{If}\:\:\:\:\:\frac{\mathrm{sin}^{\mathrm{4}} \mathrm{x}}{\mathrm{5}}\:+\:\frac{\mathrm{cos}^{\mathrm{4}} \mathrm{x}}{\mathrm{7}}\:=\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\mathrm{Find}\:\:\:\:\:\frac{\mathrm{sin}^{\mathrm{2}} \:\mathrm{2x}}{\mathrm{5}}\:+\:\frac{\mathrm{cos}^{\mathrm{2}} \:\mathrm{2x}}{\mathrm{7}}\:=\:? \\ $$

Question Number 188069 Answers: 0 Comments: 1

how is solution ∫(√e^x )ln (√e^x )dx=?

$${how}\:{is}\:{solution} \\ $$$$\int\sqrt{{e}^{{x}} }\mathrm{ln}\:\sqrt{{e}^{{x}} }{dx}=? \\ $$

Question Number 188062 Answers: 1 Comments: 8

Question Number 188060 Answers: 4 Comments: 0

Question Number 188059 Answers: 1 Comments: 0

Question Number 188037 Answers: 1 Comments: 0

find (dy/dx) y=2x^(√x)

$${find}\:\frac{{dy}}{{dx}} \\ $$$${y}=\mathrm{2}{x}^{\sqrt{{x}}} \\ $$

Question Number 188036 Answers: 1 Comments: 0

∫2^x e^x dx

$$\int\mathrm{2}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 188035 Answers: 1 Comments: 0

solve ∫(x^2 /((a+bx)^2 ))dx

$${solve} \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 188034 Answers: 1 Comments: 0

solve ∫((x^2 +3)/(x^6 (x^2 +1)))dx

$${solve} \\ $$$$\int\frac{{x}^{\mathrm{2}} +\mathrm{3}}{{x}^{\mathrm{6}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx} \\ $$

Question Number 188033 Answers: 2 Comments: 0

from first principle y=xInx find (dy/dx)

$${from}\:{first}\:{principle} \\ $$$${y}={xInx}\:\:{find}\:\frac{{dy}}{{dx}} \\ $$

Question Number 188048 Answers: 1 Comments: 0

Question Number 188017 Answers: 1 Comments: 0

Question Number 188016 Answers: 1 Comments: 0

Question Number 188012 Answers: 0 Comments: 1

Question Number 188010 Answers: 0 Comments: 0

Question Number 188000 Answers: 0 Comments: 1

Question Number 187998 Answers: 1 Comments: 0

Question Number 187993 Answers: 0 Comments: 0

prove that ∫_0 ^(π/2) ∫_0 ^(π/2) (((sin3x)/(sin2y)))^(1/3) dxdy=(π/(2(√3)))

$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt[{\mathrm{3}}]{\frac{{sin}\mathrm{3}{x}}{{sin}\mathrm{2}{y}}}{dxdy}=\frac{\pi}{\mathrm{2}\sqrt{\mathrm{3}}} \\ $$

Question Number 187989 Answers: 2 Comments: 0

Question Number 187988 Answers: 3 Comments: 0

find function f(x) and g(x) such that { ((f(2x−1)+g(1−x)=x+1)),((f((x/(x+1)))+2g((1/(2x+2)))=3)) :}

$$\:\mathrm{find}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\begin{cases}{\mathrm{f}\left(\mathrm{2x}−\mathrm{1}\right)+\mathrm{g}\left(\mathrm{1}−\mathrm{x}\right)=\mathrm{x}+\mathrm{1}}\\{\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}}\right)+\mathrm{2g}\left(\frac{\mathrm{1}}{\mathrm{2x}+\mathrm{2}}\right)=\mathrm{3}}\end{cases} \\ $$

Question Number 187984 Answers: 0 Comments: 0

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