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Question Number 147101 Answers: 1 Comments: 0

find U_n =∫_0 ^1 (1+x^2 )(1+x^4 )....(1+x^2^n )dx

$$\mathrm{find}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)....\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}^{\mathrm{n}} } \right)\mathrm{dx} \\ $$

Question Number 147100 Answers: 0 Comments: 0

findA_n = ∫_0 ^1 x(x+1)(x+2)....(x+n)dx

$$\mathrm{findA}_{\mathrm{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{2}\right)....\left(\mathrm{x}+\mathrm{n}\right)\mathrm{dx} \\ $$

Question Number 147093 Answers: 3 Comments: 2

(1)lim_(x→π/2) ((cos 4x−cos 2x−2)/((2x−π)^2 )) =? (2)lim_(x→0) ((sin 3x+sin 6x−sin 9x)/x^3 ) =? (3)lim_(x→π/4) ((sec^2 x−2tan x)/((x−(π/4))^2 )) =? (4)lim_(x→0) ((12−6x^2 −12cos x)/x^4 )=? (5)lim_(x→0) ((sin^2 x−sin^2 2x+3x^2 )/x^4 )=?

$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{4}{x}−\mathrm{cos}\:\mathrm{2}{x}−\mathrm{2}}{\left(\mathrm{2}{x}−\pi\right)^{\mathrm{2}} }\:=? \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{3}{x}+\mathrm{sin}\:\mathrm{6}{x}−\mathrm{sin}\:\mathrm{9}{x}}{{x}^{\mathrm{3}} }\:=? \\ $$$$\left(\mathrm{3}\right)\underset{{x}\rightarrow\pi/\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{sec}\:^{\mathrm{2}} {x}−\mathrm{2tan}\:{x}}{\left({x}−\frac{\pi}{\mathrm{4}}\right)^{\mathrm{2}} }\:=? \\ $$$$\left(\mathrm{4}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{12}−\mathrm{6}{x}^{\mathrm{2}} −\mathrm{12cos}\:{x}}{{x}^{\mathrm{4}} }=? \\ $$$$\left(\mathrm{5}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} }=? \\ $$

Question Number 147091 Answers: 1 Comments: 0

Question Number 147076 Answers: 2 Comments: 0

a+b+c=1 a^2 +b^2 +c^2 =1 ⇒ abc=? a^3 +b^3 +c^3 =1

$${a}+{b}+{c}=\mathrm{1} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{1}\:\:\:\:\:\Rightarrow\:\:\:{abc}=? \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{1} \\ $$

Question Number 147071 Answers: 1 Comments: 0

prove that (√(1+(√(1+(√(1+(√(1+...)))))))) = 1+(1/(1+(1/(1+(1/(1+⋱))))))

$${prove}\:{that} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+...}}}}\:=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\ddots}}} \\ $$

Question Number 147068 Answers: 1 Comments: 0

find laplase transforme of e^((t−1)^2 )

$${find}\:{laplase}\:{transforme}\:{of}\:{e}^{\left({t}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 147066 Answers: 3 Comments: 0

find laurant series lf (1)f(z)=(1/(z−1))+(1/(z+2)) ,∣z∣>1 (2)f(z)=(1/(z−2))−(2/(z−3)) ,∣z∣<3

$${find}\:{laurant}\:{series}\:{lf} \\ $$$$ \\ $$$$\:\left(\mathrm{1}\right){f}\left({z}\right)=\frac{\mathrm{1}}{{z}−\mathrm{1}}+\frac{\mathrm{1}}{{z}+\mathrm{2}}\:\:,\mid{z}\mid>\mathrm{1} \\ $$$$ \\ $$$$\left(\mathrm{2}\right){f}\left({z}\right)=\frac{\mathrm{1}}{{z}−\mathrm{2}}−\frac{\mathrm{2}}{{z}−\mathrm{3}}\:\:,\mid{z}\mid<\mathrm{3} \\ $$

Question Number 147061 Answers: 2 Comments: 0

∫_( 0 ) ^( ∞) (x^a /((1+x^3 ))) (dx/x) =? 0<a<3

$$\:\:\:\:\:\int_{\:\mathrm{0}\:} ^{\:\infty} \:\frac{{x}^{{a}} }{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)}\:\frac{{dx}}{{x}}\:=?\: \\ $$$$\:\:\mathrm{0}<{a}<\mathrm{3}\:\: \\ $$

Question Number 147060 Answers: 1 Comments: 0

∫_0 ^(π/2) e^(2x) (√(tanx))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {e}^{\mathrm{2}{x}} \sqrt{{tanx}}{dx} \\ $$

Question Number 147035 Answers: 2 Comments: 0

using residue theorem evaluate ∫_(∣z∣=3) ((zsecz)/((z−1)^2 ))dz

$${using}\:{residue}\:{theorem} \\ $$$${evaluate}\:\:\int_{\mid{z}\mid=\mathrm{3}} \frac{{zsecz}}{\left({z}−\mathrm{1}\right)^{\mathrm{2}} }{dz} \\ $$

Question Number 147031 Answers: 5 Comments: 0

Question Number 147028 Answers: 0 Comments: 0

Question Number 147022 Answers: 0 Comments: 0

Question Number 147018 Answers: 1 Comments: 1

Question Number 147015 Answers: 0 Comments: 0

Question Number 147011 Answers: 2 Comments: 3

2x - (√(2x - 3)) - 9 = 0 if there′s a solution to equation, find 4a + 3 = ?

$$\mathrm{2}{x}\:-\:\sqrt{\mathrm{2}{x}\:-\:\mathrm{3}}\:-\:\mathrm{9}\:=\:\mathrm{0} \\ $$$${if}\:{there}'{s}\:\boldsymbol{{a}}\:{solution}\:{to}\:{equation}, \\ $$$${find}\:\:\mathrm{4}\boldsymbol{{a}}\:+\:\mathrm{3}\:=\:? \\ $$

Question Number 147010 Answers: 1 Comments: 1

if the radius of a circle touching parabola y^2 =4x at (4,4)and having directrix of y^2 =4x as its normal is r, then find [r]? (where [x] denote greatest integer lessthan or equal to x)

$${if}\:{the}\:{radius}\:{of}\:{a}\:{circle}\:{touching}\: \\ $$$${parabola}\:{y}^{\mathrm{2}} =\mathrm{4}{x}\:\:{at}\:\left(\mathrm{4},\mathrm{4}\right){and}\:{having} \\ $$$${directrix}\:{of}\:{y}^{\mathrm{2}} =\mathrm{4}{x}\:{as}\:{its}\:{normal}\: \\ $$$${is}\:{r},\:{then}\:{find}\:\left[{r}\right]? \\ $$$$\left({where}\:\left[{x}\right]\:{denote}\:{greatest}\:{integer}\:\right. \\ $$$$\left.{lessthan}\:{or}\:{equal}\:{to}\:{x}\right) \\ $$

Question Number 147009 Answers: 1 Comments: 0

a parabola y=x^2 −15x+36 cuts the x axis at P and Q. a circle is drawn through P and Q so that the origin is outside it. then find the length of tangent to the circle from (0,0)?

$${a}\:{parabola}\:{y}={x}^{\mathrm{2}} −\mathrm{15}{x}+\mathrm{36}\:{cuts}\:{the}\: \\ $$$${x}\:{axis}\:{at}\:{P}\:\:{and}\:{Q}.\:{a}\:{circle}\:{is}\:{drawn} \\ $$$${through}\:{P}\:{and}\:{Q}\:{so}\:{that}\:{the}\:{origin} \\ $$$${is}\:{outside}\:{it}.\:{then}\:{find}\:{the}\:{length}\: \\ $$$${of}\:{tangent}\:{to}\:{the}\:{circle}\:{from}\:\left(\mathrm{0},\mathrm{0}\right)? \\ $$

Question Number 147006 Answers: 1 Comments: 0

find I_n =∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)......(x^2 +n)))

$$\mathrm{find}\:\:\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{2}\right)......\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{n}\right)} \\ $$

Question Number 146996 Answers: 1 Comments: 0

∫ln(cht)dt

$$\int{ln}\left({cht}\right){dt} \\ $$

Question Number 146994 Answers: 3 Comments: 0

u_n =cos(√(n+1))−cos(√n) lim_(x→+∞) u_n =??

$${u}_{{n}} ={cos}\sqrt{{n}+\mathrm{1}}−{cos}\sqrt{{n}} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{u}_{{n}} =?? \\ $$

Question Number 146989 Answers: 1 Comments: 2

Simplify: ((x^(1/2) + y^(1/2) )/(x^(1/6) + y^(1/6) )) - ((x^(1/2) - y^(1/2) )/(x^(1/6) - y^(1/6) )) = ?