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AllQuestion and Answers: Page 454

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 βˆ’x^2 )) dx

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

Question Number 167510    Answers: 1   Comments: 0

explicite f(a)=∫_0 ^(Ο€/2) ln(a+tan^2 x)dx aβ‰₯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 βˆ’1 How much the x is?

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

Question Number 167505    Answers: 0   Comments: 0

Solve this Equation : lim_(xβ†’1) (((x/(βˆ’x)))Γ—(((x/x))+((x/x)))^((((x/x))+((x/x))+((x/x)))) ) Then says it in English word, but without saying the word β€²β€²Negativeβ€²β€² That would be NSFW account on Twitter.

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

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 Ξ±=(m/(m+1)))),((tan Ξ²=(1/(2m+1)))) :}β‡’Ξ±+Ξ²=?

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

Question Number 167501    Answers: 0   Comments: 0

((tan^2 (Ο€/7)+tan^2 ((2Ο€)/7)+tan^2 ((3Ο€)/7))/(cot^2 (Ο€/7)+cot^2 ((2Ο€)/7)+cot^2 ((3Ο€)/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+(Ο€/2)) trigonometric function ?

$${is}\:{cos}\left({t}+\frac{\pi}{\mathrm{2}}\right)\:{trigonometric}\:{function}\:? \\ $$

Question Number 167533    Answers: 0   Comments: 3

Find out a,b,c where { ((a^2 +b^2 =c^2 )),((a+b+c=1000)) :}

$$\:\:\:\:\:\:\mathrm{Find}\:\mathrm{out}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{where}\:\begin{cases}{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{c}^{\mathrm{2}} }\\{\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{1000}}\end{cases}\:\:\: \\ $$

Question Number 167532    Answers: 0   Comments: 5

Question Number 167496    Answers: 0   Comments: 0

Question Number 167493    Answers: 1   Comments: 0

(√(x+6))+(√(8βˆ’x))=A x∈Z and A∈R ^( faid Ξ£x=?)

$$\sqrt{{x}+\mathrm{6}}+\sqrt{\mathrm{8}βˆ’{x}}={A} \\ $$$${x}\in{Z}\:\:\:{and}\:{A}\in{R}\:\:\:\:\:\:\:\:\:\overset{\:\:\:\:{faid}\:\:\Sigma{x}=?} {\:} \\ $$

Question Number 167492    Answers: 1   Comments: 0

x^a =(√2)+1 .........(1) x^b =(√2)βˆ’1 .........(2) (1/x^(aβˆ’b) )+(1/x^(bβˆ’a) )=? (1)Γ·(2)β‡’(x^a /x^b )=(((√2)+1)/( (√(2βˆ’1))))β‡’x^(aβˆ’b) =(((√2)+1)/( (√(2βˆ’1))))β‡’(1/x^(aβˆ’b) )=(((√2)βˆ’1)/( (√2)+1))....(3) (2)Γ·(1)β‡’(x^b /x^a )=(((√2)βˆ’1)/( (√2)+1))β‡’x^(bβˆ’a) =(((√2)βˆ’1)/( (√2)+1))β‡’(1/x^(bβˆ’a) )=(((√2)+1)/( (√2)βˆ’1))....(4) (1/x^(aβˆ’b) )+(1/x^(bβˆ’a) )=(((√2)βˆ’1)/( (√2)+1))+(((√2)+1)/( (√2)βˆ’1))=((((√2)βˆ’1)((√2)βˆ’1)+((√2)+1)((√2)+1))/(((√2)+1)((√2)βˆ’1))) =((((√2)βˆ’1)^2 +((√2)+1)^2 )/(2βˆ’1))=2βˆ’2(√2)+1+2+2(√2)+1 (1/x^(aβˆ’b) )+(1/x^(bβˆ’a) )=6

$${x}^{{a}} =\sqrt{\mathrm{2}}+\mathrm{1}\:\:\:\:\:.........\left(\mathrm{1}\right)\: \\ $$$${x}^{{b}} =\sqrt{\mathrm{2}}βˆ’\mathrm{1}\:\:\:\:\:.........\left(\mathrm{2}\right) \\ $$$$\frac{\mathrm{1}}{{x}^{{a}βˆ’{b}} }+\frac{\mathrm{1}}{{x}^{{b}βˆ’{a}} }=? \\ $$$$\left(\mathrm{1}\right)\boldsymbol{\div}\left(\mathrm{2}\right)\Rightarrow\frac{{x}^{{a}} }{{x}^{{b}} }=\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}βˆ’\mathrm{1}}}\Rightarrow{x}^{{a}βˆ’{b}} =\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}βˆ’\mathrm{1}}}\Rightarrow\frac{\mathrm{1}}{{x}^{{a}βˆ’{b}} }=\frac{\sqrt{\mathrm{2}}βˆ’\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}....\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{2}\right)\boldsymbol{\div}\left(\mathrm{1}\right)\Rightarrow\frac{{x}^{{b}} }{{x}^{{a}} }=\frac{\sqrt{\mathrm{2}}βˆ’\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}\Rightarrow{x}^{{b}βˆ’{a}} =\frac{\sqrt{\mathrm{2}}βˆ’\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}\Rightarrow\frac{\mathrm{1}}{{x}^{{b}βˆ’{a}} }=\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}}βˆ’\mathrm{1}}....\left(\mathrm{4}\right) \\ $$$$\frac{\mathrm{1}}{{x}^{{a}βˆ’{b}} }+\frac{\mathrm{1}}{{x}^{{b}βˆ’{a}} }=\frac{\sqrt{\mathrm{2}}βˆ’\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}+\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}}βˆ’\mathrm{1}}=\frac{\left(\sqrt{\mathrm{2}}βˆ’\mathrm{1}\right)\left(\sqrt{\mathrm{2}}βˆ’\mathrm{1}\right)+\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)}{\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}βˆ’\mathrm{1}\right)} \\ $$$$=\frac{\left(\sqrt{\mathrm{2}}βˆ’\mathrm{1}\right)^{\mathrm{2}} +\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{2}βˆ’\mathrm{1}}=\mathrm{2}βˆ’\cancel{\mathrm{2}\sqrt{\mathrm{2}}}+\mathrm{1}+\mathrm{2}+\cancel{\mathrm{2}\sqrt{\mathrm{2}}}+\mathrm{1} \\ $$$$\frac{\mathrm{1}}{{x}^{{a}βˆ’{b}} }+\frac{\mathrm{1}}{{x}^{{b}βˆ’{a}} }=\mathrm{6} \\ $$

Question Number 167490    Answers: 1   Comments: 0

∫sin^3 xcos^2 xdx=?

$$\int{sin}^{\mathrm{3}} {xcos}^{\mathrm{2}} {xdx}=? \\ $$

Question Number 167489    Answers: 1   Comments: 0

a+(√x)=2 b+(x)^(1/4) =9 ^( (4aβˆ’b^2 )=?)

$${a}+\sqrt{{x}}=\mathrm{2} \\ $$$${b}+\sqrt[{\mathrm{4}}]{{x}}=\mathrm{9}\:\:\:\:\:\:\:\:\:\overset{\:\:\:\:\:\:\left(\mathrm{4}{a}βˆ’{b}^{\mathrm{2}} \right)=?} {\:} \\ $$

Question Number 167488    Answers: 1   Comments: 1

a^2 βˆ’4a+2=0 a≻2 (√((a^4 +4)/(12a^2 )))=?

$${a}^{\mathrm{2}} βˆ’\mathrm{4}{a}+\mathrm{2}=\mathrm{0}\:\:\:\:\:\:\:\:\:{a}\succ\mathrm{2} \\ $$$$\sqrt{\frac{{a}^{\mathrm{4}} +\mathrm{4}}{\mathrm{12}{a}^{\mathrm{2}} }}=? \\ $$

Question Number 167486    Answers: 1   Comments: 0

cos^2 x = cos (((4x)/3)) ; 0≀x≀2Ο€

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} {x}\:=\:\mathrm{cos}\:\left(\frac{\mathrm{4}{x}}{\mathrm{3}}\right)\:;\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi \\ $$

Question Number 167485    Answers: 1   Comments: 0

∫∫∫x^n dx

$$\int\int\int\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{dx}} \\ $$

Question Number 167484    Answers: 0   Comments: 0

∫_0 ^1 ln(x)cos^(βˆ’1) (x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{cos}}^{βˆ’\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$

Question Number 167482    Answers: 0   Comments: 0

montrer que βˆ€x∈Rβˆ’{0; 1} on a ((ln(x))/(xβˆ’1)) < (1/( (√x))) ?

$$\mathrm{montrer}\:\mathrm{que}\:\forall\mathrm{x}\in\mathbb{R}βˆ’\left\{\mathrm{0};\:\mathrm{1}\right\}\:\mathrm{on}\:\mathrm{a} \\ $$$$\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}βˆ’\mathrm{1}}\:<\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\:? \\ $$

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