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Question Number 167586 Answers: 2 Comments: 1

λ=∫ (dx/( (√(1+cos x))+(√(1+sin x)))) =?

$$\:\:\:\:\:\:\:\:\lambda=\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}+\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}\:=? \\ $$

Question Number 167628 Answers: 0 Comments: 1

Question Number 167627 Answers: 0 Comments: 0

Question Number 167576 Answers: 1 Comments: 1

prove by useing the polar cordinaite ∫_0 ^( (a/2)) ∫_y ^( (√(a^2 −y^2 ))) x dx dy = ((5 a^3 )/(24 ))

$$\boldsymbol{{prove}}\:\boldsymbol{{by}}\:\boldsymbol{{useing}}\:\boldsymbol{{the}}\:\boldsymbol{{polar}}\:\boldsymbol{{cordinaite}}\: \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{{a}}}{\mathrm{2}}} \:\:\:\int_{\boldsymbol{{y}}} ^{\:\sqrt{\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{y}}^{\mathrm{2}} }} \:\boldsymbol{{x}}\:\boldsymbol{{dx}}\:\boldsymbol{{dy}}\:\:=\:\frac{\mathrm{5}\:\boldsymbol{{a}}^{\mathrm{3}} }{\mathrm{24}\:} \\ $$

Question Number 167567 Answers: 1 Comments: 3

Find the coordinates of the point on the curve y=3x^2 −2x−5, where the tangent is parallel to the line y−5=8x.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{coordinates}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{curve}\:\mathrm{y}=\mathrm{3x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{5},\:\mathrm{where}\:\mathrm{the}\:\mathrm{tangent} \\ $$$$\mathrm{is}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}−\mathrm{5}=\mathrm{8x}. \\ $$

Question Number 167566 Answers: 1 Comments: 0

Question Number 167562 Answers: 1 Comments: 0

∫ (e^(−x) /(1+e^x )) dx=?

$$\:\:\:\:\:\:\:\:\int\:\frac{{e}^{−{x}} }{\mathrm{1}+{e}^{{x}} }\:{dx}=? \\ $$

Question Number 167554 Answers: 3 Comments: 0

∫_0 ^∞ ((3x^2 )/( (√((5x^2 +1)^3 )))) dx

$$\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{3x}^{\mathrm{2}} }{\:\sqrt{\left(\mathrm{5x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }}\:\mathrm{dx} \\ $$$$ \\ $$

Question Number 167550 Answers: 2 Comments: 0

Question Number 167549 Answers: 0 Comments: 0

Question Number 167547 Answers: 0 Comments: 1

Question Number 167526 Answers: 1 Comments: 1

∫_0 ^(𝛑/2) 𝚺_(n=1) ^∞ (1/(n^2 +1))dn=???

$$\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} +\mathrm{1}}\boldsymbol{\mathrm{dn}}=??? \\ $$

Question Number 167534 Answers: 0 Comments: 0

Question Number 167520 Answers: 1 Comments: 0

Given that f(x) = ∫_x ^(2x) (1/( (√(1+t^4 ))))dt (a) state its domain (b) is f(x) even or odd?

$$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)\:=\:\int_{{x}} ^{\mathrm{2}{x}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{t}^{\mathrm{4}} }}{dt} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{state}\:\mathrm{its}\:\mathrm{domain} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{is}\:{f}\left({x}\right)\:\mathrm{even}\:\mathrm{or}\:\mathrm{odd}? \\ $$

Question Number 167517 Answers: 1 Comments: 0

𝚺_(n=1) ^∞ ((cos(n)sin(n))/(tan(n)))

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{n}}\right)\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{n}}\right)}{\boldsymbol{\mathrm{tan}}\left(\boldsymbol{\mathrm{n}}\right)} \\ $$

Question Number 167512 Answers: 1 Comments: 2

∫_0 ^r (√(r^2 −x^2 )) dx

$$\int_{\mathrm{0}} ^{{r}} \sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 167510 Answers: 1 Comments: 0

explicite f(a)=∫_0 ^(π/2) ln(a+tan^2 x)dx a≥2

$${explicite}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({a}+{tan}^{\mathrm{2}} {x}\right){dx} \\ $$$${a}\geqslant\mathrm{2} \\ $$

Question Number 167508 Answers: 2 Comments: 0

2((2x+1))^(1/3) =x^3 −1 How much the x is?

$$\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{2}{x}+\mathrm{1}}={x}^{\mathrm{3}} −\mathrm{1} \\ $$$${How}\:{much}\:{the}\:{x}\:{is}? \\ $$

Question Number 167505 Answers: 0 Comments: 0

Solve this Equation : lim_(x→1) (((x/(−x)))×(((x/x))+((x/x)))^((((x/x))+((x/x))+((x/x)))) ) Then says it in English word, but without saying the word ′′Negative′′ That would be NSFW account on Twitter.

$${Solve}\:{this}\:{Equation}\:: \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\left(\frac{{x}}{−{x}}\right)×\left(\left(\frac{{x}}{{x}}\right)+\left(\frac{{x}}{{x}}\right)\right)^{\left(\left(\frac{{x}}{{x}}\right)+\left(\frac{{x}}{{x}}\right)+\left(\frac{{x}}{{x}}\right)\right)} \right) \\ $$$${Then}\:{says}\:{it}\:{in}\:{English}\:{word},\: \\ $$$${but}\:{without}\:{saying}\:{the}\:{word}\: \\ $$$$''\boldsymbol{{N}}{egative}'' \\ $$$${That}\:{would}\:{be}\:{NSFW}\:{account}\:{on} \\ $$$${Twitter}. \\ $$

Question Number 167519 Answers: 0 Comments: 0

V_4 is a set of all real valued continues functions defined on the entire real line together with standard addition and scalar multiplication. Is V_4 a vector space? Explain

$$\mathcal{V}_{\mathrm{4}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{real}\:\mathrm{valued}\:\mathrm{continues}\: \\ $$$$\mathrm{functions}\:\mathrm{defined}\:\mathrm{on}\:\mathrm{the}\:\mathrm{entire}\:\mathrm{real} \\ $$$$\mathrm{line}\:\mathrm{together}\:\mathrm{with}\:\mathrm{standard}\:\mathrm{addition} \\ $$$$\mathrm{and}\:\mathrm{scalar}\:\mathrm{multiplication}.\:\mathrm{Is}\:\mathcal{V}_{\mathrm{4}} \: \\ $$$$\mathrm{a}\:\mathrm{vector}\:\mathrm{space}?\:\mathrm{Explain} \\ $$

Question Number 167502 Answers: 1 Comments: 0

{ ((tan α=(m/(m+1)))),((tan β=(1/(2m+1)))) :}⇒α+β=?

$$\:\:\:\:\:\:\begin{cases}{\mathrm{tan}\:\alpha=\frac{\mathrm{m}}{\mathrm{m}+\mathrm{1}}}\\{\mathrm{tan}\:\beta=\frac{\mathrm{1}}{\mathrm{2m}+\mathrm{1}}}\end{cases}\Rightarrow\alpha+\beta=? \\ $$

Question Number 167501 Answers: 0 Comments: 0

((tan^2 (π/7)+tan^2 ((2π)/7)+tan^2 ((3π)/7))/(cot^2 (π/7)+cot^2 ((2π)/7)+cot^2 ((3π)/7))) =?

$$\:\:\:\:\:\:\frac{\mathrm{tan}\:^{\mathrm{2}} \frac{\pi}{\mathrm{7}}+\mathrm{tan}\:^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{7}}+\mathrm{tan}\:^{\mathrm{2}} \frac{\mathrm{3}\pi}{\mathrm{7}}}{\mathrm{cot}\:^{\mathrm{2}} \frac{\pi}{\mathrm{7}}+\mathrm{cot}\:^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{7}}+\mathrm{cot}\:^{\mathrm{2}} \frac{\mathrm{3}\pi}{\mathrm{7}}}\:=? \\ $$

Question Number 167539 Answers: 2 Comments: 0

Suppose x and y are real, such that, log_4 x = log_6 y = log_9 (x + y), find (y/x)

$$\mathrm{Suppose}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{are}\:\mathrm{real},\:\mathrm{such}\:\mathrm{that},\:\:\:\mathrm{log}_{\mathrm{4}} \mathrm{x}\:\:\:=\:\:\:\mathrm{log}_{\mathrm{6}} \mathrm{y}\:\:\:=\:\:\:\mathrm{log}_{\mathrm{9}} \left(\mathrm{x}\:+\:\mathrm{y}\right), \\ $$$$\mathrm{find}\:\:\:\frac{\mathrm{y}}{\mathrm{x}} \\ $$

Question Number 167536 Answers: 0 Comments: 4

is cos(t+(π/2)) trigonometric function ?