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Relation and FunctionsQuestion and Answers: Page 13

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 141220 Answers: 2 Comments: 0

calculate ∫_0 ^∞ ((logx)/(1+x^4 )) dx

$$\mathrm{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{logx}}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\:\mathrm{dx} \\ $$

Question Number 141219 Answers: 1 Comments: 0

find ∫∫_([0,1]^2 ) e^(−(x^2 +y^2 )) (√(x^4 +y^4 ))dxdy

$$\mathrm{find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\mathrm{e}^{−\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)} \sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{y}^{\mathrm{4}} }\mathrm{dxdy} \\ $$

Question Number 141218 Answers: 3 Comments: 0

calculate I =∫_0 ^(π/2) ^4 (√(tanx))log(tanx)dx and J =∫_0 ^(π/2) ((log(tanx))/((^3 (√(tanx)))))dx

$$\mathrm{calculate}\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:^{\mathrm{4}} \sqrt{\mathrm{tanx}}\mathrm{log}\left(\mathrm{tanx}\right)\mathrm{dx}\:\:\mathrm{and} \\ $$$$\mathrm{J}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{log}\left(\mathrm{tanx}\right)}{\left(^{\mathrm{3}} \sqrt{\mathrm{tanx}}\right)}\mathrm{dx} \\ $$

Question Number 140982 Answers: 0 Comments: 3

convergence and value of Σ_(n=1) ^∞ (n^n /((n!)^2 ))

$${convergence}\:{and}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{n}^{{n}} }{\left({n}!\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$

Question Number 140978 Answers: 1 Comments: 0

calculate Σ_(n=0) ^∞ (1/((n!)^2 ))

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\left({n}!\right)^{\mathrm{2}} } \\ $$

Question Number 140958 Answers: 0 Comments: 0

find e^ (((−1 1)),((2 −1)) )

$$\mathrm{find}\:\mathrm{e}^{\begin{pmatrix}{−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{1}}\end{pmatrix}} \\ $$

Question Number 140828 Answers: 2 Comments: 0

factorise 3k^2 +2kh−8h^2

$$\mathrm{factorise}\:\mathrm{3k}^{\mathrm{2}} \:+\mathrm{2kh}−\mathrm{8h}^{\mathrm{2}} \\ $$

Question Number 140748 Answers: 3 Comments: 0

Question Number 140747 Answers: 0 Comments: 0

Question Number 140638 Answers: 3 Comments: 0

let f(x)=arctan((2/x)) developp f at integr serie

$${let}\:{f}\left({x}\right)={arctan}\left(\frac{\mathrm{2}}{{x}}\right) \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 140637 Answers: 1 Comments: 0

let f(x)=x^(2n) e^(−3x) find f^((n)) (o) and calculate f^((2021)) (0)

$${let}\:{f}\left({x}\right)={x}^{\mathrm{2}{n}} \:{e}^{−\mathrm{3}{x}} \\ $$$${find}\:\:{f}^{\left({n}\right)} \left({o}\right)\:{and} \\ $$$${calculate}\:{f}^{\left(\mathrm{2021}\right)} \left(\mathrm{0}\right) \\ $$

Question Number 140636 Answers: 2 Comments: 0

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^2 (n+1)(2n+1)^2 ))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 140531 Answers: 1 Comments: 0

Prove that ∫^( x) _0 (t/(e^t −1)) dt = Σ_(n=1) ^(+∞) (((1−e^(−x) )^n )/n^2 )

$$\mathrm{Prove}\:\mathrm{that}\:\:\underset{\mathrm{0}} {\int}^{\:\mathrm{x}} \:\frac{\mathrm{t}}{\mathrm{e}^{\mathrm{t}} −\mathrm{1}}\:\mathrm{dt}\:=\:\underset{\mathrm{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\:\frac{\left(\mathrm{1}−\mathrm{e}^{−\mathrm{x}} \right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$

Question Number 140470 Answers: 2 Comments: 0

(f(x))^2 . f(((1−x)/(1+x))) = 64x , ∀x∈D ⇒ f(x) =?

$$\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} .\:\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\:=\:\mathrm{64x}\:,\:\forall\mathrm{x}\in\mathrm{D} \\ $$$$\Rightarrow\:\mathrm{f}\left(\mathrm{x}\right)\:=? \\ $$

Question Number 140387 Answers: 1 Comments: 0

Question Number 140325 Answers: 1 Comments: 0

What is the equation of the circle, if the circle is tangential to the line 3x+y+2=0 at (-1,1) and it passes through the point (3,5)?

$$ \\ $$What is the equation of the circle, if the circle is tangential to the line 3x+y+2=0 at (-1,1) and it passes through the point (3,5)?

Question Number 140076 Answers: 2 Comments: 6

Question Number 140073 Answers: 1 Comments: 0

Let f(x)= { ((3x^2 −1 ; x<0)),((cx+d ; 0≤x≤1)),(((√(x+8)) ; x>1)) :} find the value of c & d such that f(x) continous everywhere

$$\mathrm{Let}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{3x}^{\mathrm{2}} −\mathrm{1}\:;\:\mathrm{x}<\mathrm{0}}\\{\mathrm{cx}+\mathrm{d}\:;\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{1}}\\{\sqrt{\mathrm{x}+\mathrm{8}}\:;\:\mathrm{x}>\mathrm{1}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{c}\:\&\:\mathrm{d}\:\mathrm{such}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{continous} \\ $$$$\mathrm{everywhere} \\ $$

Question Number 140071 Answers: 1 Comments: 0

For what value of k is the following continous function ? f(x)= { (((((√(7x+2))−(√(6x+4)))/(x−2)) ; if x≥−(2/7) & x≠2)),(( k ; if x=2)) :}

$$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{is}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{continous}\:\mathrm{function}\:? \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\frac{\sqrt{\mathrm{7x}+\mathrm{2}}−\sqrt{\mathrm{6x}+\mathrm{4}}}{\mathrm{x}−\mathrm{2}}\:;\:\mathrm{if}\:\mathrm{x}\geqslant−\frac{\mathrm{2}}{\mathrm{7}}\:\&\:\mathrm{x}\neq\mathrm{2}}\\{\:\:\:\:\:\:\:\:\mathrm{k}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:;\:\mathrm{if}\:\mathrm{x}=\mathrm{2}}\end{cases} \\ $$

Question Number 139954 Answers: 2 Comments: 0

Question Number 139711 Answers: 0 Comments: 2

[f(x)]^2 −[f(−x)]^2 =4x

$$\:\left[\mathrm{f}\left(\mathrm{x}\right)\right]^{\mathrm{2}} −\left[\mathrm{f}\left(−\mathrm{x}\right)\right]^{\mathrm{2}} =\mathrm{4x} \\ $$

Question Number 139639 Answers: 1 Comments: 1

What is the reflection of the point (2,2) in the line x+2y = 4?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{reflection}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{point}\:\left(\mathrm{2},\mathrm{2}\right)\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:\mathrm{x}+\mathrm{2y}\:=\:\mathrm{4}? \\ $$

Question Number 139612 Answers: 1 Comments: 0

show that ∫_0 ^( ∞) ((cos((√x)))/(e^(2π(√x)) −1))dx = 1−(e/((e−1)^2 ))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left(\sqrt{{x}}\right)}{{e}^{\mathrm{2}\pi\sqrt{{x}}} −\mathrm{1}}{dx}\:=\:\mathrm{1}−\frac{{e}}{\left({e}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 139592 Answers: 2 Comments: 0

Given f(x)=(√(2+x^2 −x)) +(√(2−x^2 )) If (g○f)(x) = 2x+1 then g^(−1) (−1)=?

$$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}} −\mathrm{x}}\:+\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{If}\:\left(\mathrm{g}\circ\mathrm{f}\right)\left(\mathrm{x}\right)\:=\:\mathrm{2x}+\mathrm{1}\:\mathrm{then}\:\mathrm{g}^{−\mathrm{1}} \left(−\mathrm{1}\right)=? \\ $$

Question Number 139032 Answers: 1 Comments: 0

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