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Question Number 142903 Answers: 0 Comments: 0

Question Number 142893 Answers: 1 Comments: 0

.....mathematical .....analysis...... f ∈ C [0,1] and ∫_0 ^( 1) x^n f(x)dx=(1/(n+2)) , n∈N prove f(x):=x .....

$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:.....{mathematical}\:.....{analysis}...... \\ $$$$\:\:\:\:\:\:\:{f}\:\in\:{C}\:\left[\mathrm{0},\mathrm{1}\right]\:{and}\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{{n}} {f}\left({x}\right){dx}=\frac{\mathrm{1}}{{n}+\mathrm{2}}\:,\:{n}\in\mathbb{N} \\ $$$$\:\:\:\:\:\:\:\:{prove}\:\:{f}\left({x}\right):={x}\:..... \\ $$

Question Number 142886 Answers: 2 Comments: 0

Evaluate ∫_0 ^( (1/2)) ((4x^2 )/( (√(1−x^2 )) )) dx

$$\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{4}{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:}\:{dx} \\ $$

Question Number 142882 Answers: 2 Comments: 1

Question Number 142880 Answers: 1 Comments: 0

Prove that 𝛗(n)=nΠ_k (1−(1/p_k )) φ(n):Euler totient function

$$\:{Prove}\:{that}\:\boldsymbol{\phi}\left({n}\right)={n}\underset{{k}} {\prod}\left(\mathrm{1}−\frac{\mathrm{1}}{{p}_{{k}} }\right)\:\:\phi\left({n}\right):{Euler}\:{totient}\:{function} \\ $$

Question Number 142875 Answers: 1 Comments: 0

Prove that ζ(s)=Π_(prime) (1/(1−p^(−s) ))

$${Prove}\:{that}\:\zeta\left({s}\right)=\underset{{prime}} {\prod}\:\frac{\mathrm{1}}{\mathrm{1}−{p}^{−{s}} } \\ $$

Question Number 142871 Answers: 0 Comments: 0

determine arctan(x+iy) at form u(x,y)+iv(x,y)

$$\mathrm{determine}\:\mathrm{arctan}\left(\mathrm{x}+\mathrm{iy}\right)\:\mathrm{at}\:\mathrm{form}\:\mathrm{u}\left(\mathrm{x},\mathrm{y}\right)+\mathrm{iv}\left(\mathrm{x},\mathrm{y}\right) \\ $$

Question Number 142870 Answers: 1 Comments: 0

Question Number 142869 Answers: 2 Comments: 0

calculate ∫_(−∞) ^(+∞) ((x^2 dx)/((x^2 −x+3)^2 ))

$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 142863 Answers: 1 Comments: 0

Question Number 142854 Answers: 0 Comments: 1

The maximum value of y=(√((x−3)^2 +(x^2 −2)^2 ))−(√(x^2 +(x−1)^2 )) is

$$\:\:{The}\:{maximum}\:{value}\:{of}\: \\ $$$$\:{y}=\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({x}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{2}} }−\sqrt{{x}^{\mathrm{2}} +\left({x}−\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$$$\:{is}\: \\ $$

Question Number 142849 Answers: 1 Comments: 0

Question Number 142858 Answers: 1 Comments: 2

Question Number 142844 Answers: 2 Comments: 0

Given that f(sin x)=cos x, evaluate f ′(sin 45°).

$$\mathrm{Given}\:\mathrm{that}\:{f}\left(\mathrm{sin}\:{x}\right)=\mathrm{cos}\:{x},\:\mathrm{evaluate} \\ $$$${f}\:'\left(\mathrm{sin}\:\mathrm{45}°\right). \\ $$

Question Number 142829 Answers: 3 Comments: 0

Find the simplest form for T = (√(1+(√(−3)))) +(√(1−(√(−3))))

$$\:{Find}\:{the}\:{simplest}\:{form}\:{for}\: \\ $$$$\:\:{T}\:=\:\sqrt{\mathrm{1}+\sqrt{−\mathrm{3}}}\:+\sqrt{\mathrm{1}−\sqrt{−\mathrm{3}}}\: \\ $$

Question Number 142822 Answers: 1 Comments: 0

Question Number 142820 Answers: 0 Comments: 1

find k if : C_n ^k =n+1

$${find}\:{k}\:{if}\::\:{C}_{{n}} ^{{k}} ={n}+\mathrm{1} \\ $$

Question Number 142805 Answers: 0 Comments: 0

Question Number 142802 Answers: 1 Comments: 1

x=2w(e^(−1) )

$${x}=\mathrm{2}{w}\left({e}^{−\mathrm{1}} \right) \\ $$

Question Number 142794 Answers: 3 Comments: 0

If 2cos (((5π)/4)+3x)cos ((π/4)+3x)=0 and sin (2x−2y)=cos y where (π/4)≤x≤(π/2) and (π/4)≤y≤(π/2) . find the value of { ((sin (2x+y))),((cos (2x+y))),((cos (2x−y))),((sin (2x−y))) :}

$$\mathrm{If}\:\mathrm{2cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}}+\mathrm{3x}\right)\mathrm{cos}\:\left(\frac{\pi}{\mathrm{4}}+\mathrm{3x}\right)=\mathrm{0}\:\mathrm{and}\: \\ $$$$\mathrm{sin}\:\left(\mathrm{2x}−\mathrm{2y}\right)=\mathrm{cos}\:\mathrm{y}\:\mathrm{where}\:\frac{\pi}{\mathrm{4}}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}\:\mathrm{and} \\ $$$$\frac{\pi}{\mathrm{4}}\leqslant\mathrm{y}\leqslant\frac{\pi}{\mathrm{2}}\:.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\begin{cases}{\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{y}\right)}\\{\mathrm{cos}\:\left(\mathrm{2x}+\mathrm{y}\right)}\\{\mathrm{cos}\:\left(\mathrm{2x}−\mathrm{y}\right)}\\{\mathrm{sin}\:\left(\mathrm{2x}−\mathrm{y}\right)}\end{cases} \\ $$

Question Number 142791 Answers: 1 Comments: 0

Evaluate:: ... Ω :=∫_0 ^( 1) ((li_2 ((√x) ))/(1+(√x))) dx=?? ...........

$$\:\:\:{Evaluate}::\:... \\ $$$$\:\:\:\:\:\:\:\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{li}_{\mathrm{2}} \left(\sqrt{{x}}\:\right)}{\mathrm{1}+\sqrt{{x}}}\:{dx}=?? \\ $$$$\:\:\:\:........... \\ $$

Question Number 142789 Answers: 2 Comments: 0

∫e^(x^2 /2) dx = ??

$$\int{e}^{\frac{{x}^{\mathrm{2}} }{\mathrm{2}}} \:{dx}\:=\:?? \\ $$

Question Number 142788 Answers: 1 Comments: 0

Question Number 142777 Answers: 0 Comments: 2

Question Number 142773 Answers: 2 Comments: 0

.......nice ......integral...... 𝛗:=∫_(0 ) ^( 1) ((li_2 (1−x))/(2−x)) dx=?? .......m.n...

$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:.......{nice}\:......{integral}...... \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \frac{{li}_{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{\mathrm{2}−{x}}\:{dx}=?? \\ $$$$\:.......{m}.{n}... \\ $$

Question Number 142755 Answers: 1 Comments: 2

log_3 x^3 +log_2 x^2 =((2lg6)/(lg2))+1 find x

$$\mathrm{log}_{\mathrm{3}} \mathrm{x}^{\mathrm{3}} +\mathrm{log}_{\mathrm{2}} \mathrm{x}^{\mathrm{2}} =\frac{\mathrm{2lg6}}{\mathrm{lg2}}+\mathrm{1}\:\:\mathrm{find}\:\:\mathrm{x} \\ $$

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