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Question Number 141423    Answers: 1   Comments: 0

tan (x+y)= ((12)/5) sin (x−y) = (3/5) x+y , x−y are acute angles . tan x tan y = ?

$$\mathrm{tan}\:\left({x}+{y}\right)=\:\frac{\mathrm{12}}{\mathrm{5}} \\ $$$$\mathrm{sin}\:\left({x}−{y}\right)\:=\:\frac{\mathrm{3}}{\mathrm{5}} \\ $$$${x}+{y}\:,\:{x}−{y}\:\:{are}\:\:{acute}\:\:{angles}\:. \\ $$$$\mathrm{tan}\:{x}\:\mathrm{tan}\:{y}\:=\:\:? \\ $$

Question Number 141400    Answers: 3   Comments: 0

fjnd inverse of matrix [(2,(−5)),(1,3) ]

$${fjnd}\:{inverse}\:{of}\:{matrix}\begin{bmatrix}{\mathrm{2}}&{−\mathrm{5}}\\{\mathrm{1}}&{\mathrm{3}}\end{bmatrix} \\ $$

Question Number 141398    Answers: 0   Comments: 0

Question Number 141395    Answers: 1   Comments: 0

A 64.00 cm3 piece of wood is in the shape of a cube. A lazy ant wants to walk from one corner to the very opposite corner of the cube. What is its minimum path length?

$$ \\ $$A 64.00 cm3 piece of wood is in the shape of a cube. A lazy ant wants to walk from one corner to the very opposite corner of the cube. What is its minimum path length?

Question Number 141365    Answers: 1   Comments: 0

log _(9/4) ((1/(2(√3)))(√(6−(1/(2(√3)))(√(6−(1/(2(√3)))(√(6−(1/(2(√3)))(√(...))))))))) =?

$$\:\mathrm{log}\:_{\frac{\mathrm{9}}{\mathrm{4}}} \left(\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{...}}}}\right)\:=? \\ $$

Question Number 141360    Answers: 0   Comments: 1

∫_0 ^(π/2) (√(cosxsenx))dx

$$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \sqrt{{cosxsenx}}{dx} \\ $$

Question Number 141359    Answers: 0   Comments: 2

Question Number 141356    Answers: 2   Comments: 0

lim_(x→+∞) (((x+1)/( (√(x^2 +1)))) −1)

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:−\mathrm{1}\right) \\ $$

Question Number 141362    Answers: 1   Comments: 0

∫sen(2θ)cos^4 (2θ)dθ

$$\int{sen}\left(\mathrm{2}\theta\right){cos}^{\mathrm{4}} \left(\mathrm{2}\theta\right){d}\theta \\ $$

Question Number 141352    Answers: 1   Comments: 0

Question Number 141346    Answers: 1   Comments: 0

Question Number 141345    Answers: 0   Comments: 0

((log(ζ(s)))/s)=∫_1 ^∞ J(x)x^(−s−1) dx ( Prove that) Here J(x)=π(x)+(1/2)π((√x))+(1/3)π((x)^(1/3) )+... π(x):=Prime counting function

$$\frac{{log}\left(\zeta\left({s}\right)\right)}{{s}}=\int_{\mathrm{1}} ^{\infty} {J}\left({x}\right){x}^{−{s}−\mathrm{1}} {dx}\:\left(\:{Prove}\:{that}\right) \\ $$$${Here}\:\:{J}\left({x}\right)=\pi\left({x}\right)+\frac{\mathrm{1}}{\mathrm{2}}\pi\left(\sqrt{{x}}\right)+\frac{\mathrm{1}}{\mathrm{3}}\pi\left(\sqrt[{\mathrm{3}}]{{x}}\right)+... \\ $$$$\pi\left({x}\right):=\boldsymbol{\mathrm{P}{rime}}\:\boldsymbol{{counting}}\:\boldsymbol{{function}} \\ $$

Question Number 141340    Answers: 0   Comments: 0

Given the function f defined by f(x) = { ((((2e^x )/(e^x −1)),x≠ 0)),((0, x = 0)) :} (i) study the differentiability of f at x = 0. (ii) Show that the point (0,1) is the centre of symetry to the curve of f.

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:{f}\:\mathrm{defined}\:\mathrm{by} \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{\frac{\mathrm{2}{e}^{{x}} }{{e}^{{x}} −\mathrm{1}},{x}\neq\:\mathrm{0}}\\{\mathrm{0},\:{x}\:=\:\mathrm{0}}\end{cases} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{study}\:\mathrm{the}\:\mathrm{differentiability}\:\mathrm{of}\:{f}\:\mathrm{at}\:{x}\:=\:\mathrm{0}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{0},\mathrm{1}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{symetry}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{curve}\:\mathrm{of}\:{f}. \\ $$

Question Number 141336    Answers: 2   Comments: 0

∫sin (ln (x))dx=? Please

$$\int\mathrm{sin}\:\left(\mathrm{ln}\:\left({x}\right)\right){dx}=?\:\:{Please} \\ $$

Question Number 141417    Answers: 2   Comments: 0

........ advanced ... ... ... calculus....... prove that:: F:= ∫_(−1) ^( 0) ((e^x +e^(1/x) −1)/x) dx=^(??) γ

$$\:\:\:\:\:\:\:\:\:\:........\:{advanced}\:...\:...\:...\:{calculus}....... \\ $$$$\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\mathscr{F}:=\:\int_{−\mathrm{1}} ^{\:\mathrm{0}} \frac{{e}^{{x}} +{e}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{{x}}\:{dx}\overset{??} {=}\gamma \\ $$

Question Number 141414    Answers: 0   Comments: 1

Question Number 141413    Answers: 1   Comments: 0

∫^( +∞) _( 1) ((1/(E(x)))−(1/x))dx=???

$$\underset{\:\mathrm{1}} {\int}^{\:+\infty} \left(\frac{\mathrm{1}}{\mathrm{E}\left(\mathrm{x}\right)}−\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{dx}=??? \\ $$

Question Number 141333    Answers: 1   Comments: 0

∫x^2 cos ((x/2))dx

$$\int{x}^{\mathrm{2}} \mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right){dx} \\ $$

Question Number 141323    Answers: 1   Comments: 0

Question Number 141322    Answers: 0   Comments: 0

......advanced........calculus....... prove that:: ξ:=Π_(n=2) ^∞ e(1−(1/n^2 ))^n^2 =(π/(e(√e)))

$$\:\:\:\:\:......{advanced}........{calculus}....... \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\:\:\xi:=\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } =\frac{\pi}{{e}\sqrt{{e}}} \\ $$$$ \\ $$

Question Number 141320    Answers: 1   Comments: 0

......nice ......calculuus..... prove that:: 𝛗:=∫_0 ^( ∞) ∫_0 ^( ∞) ((A rctan(x^2 y^2 ))/(x^4 +y^4 ))dxdy=((π^2 (√2))/(16)) .....

$$\:\:\:\:\:\:\:......{nice}\:......{calculuus}..... \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \frac{\mathscr{A}\:{rctan}\left({x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)}{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }{dxdy}=\frac{\pi^{\mathrm{2}} \sqrt{\mathrm{2}}}{\mathrm{16}} \\ $$$$..... \\ $$

Question Number 141319    Answers: 2   Comments: 0

prove:: Ω:=∫_0 ^( 1) ((ln^2 (x))/(1−x^4 ))dx =(π^3 /(32))+(7/8)ζ(3)..

$$\:\:\: \\ $$$$\:\:\:\:\:{prove}:: \\ $$$$\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}−{x}^{\mathrm{4}} }{dx}\:=\frac{\pi^{\mathrm{3}} }{\mathrm{32}}+\frac{\mathrm{7}}{\mathrm{8}}\zeta\left(\mathrm{3}\right).. \\ $$

Question Number 141313    Answers: 0   Comments: 0

Question Number 141383    Answers: 1   Comments: 0

sin^2 (((f(x))/2))=1−(1/2)(√(1−x^2 )) find f(x)

$$\mathrm{sin}^{\mathrm{2}} \left(\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{2}}\right)=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 141373    Answers: 1   Comments: 1

Question Number 141372    Answers: 3   Comments: 0

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