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Question Number 162509 Answers: 0 Comments: 0

find Σ_(n=1) ^∞ (((−1)^n )/(n^3 (2n+1)^4 ))

$$\mathrm{find}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} \left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$

Question Number 162399 Answers: 1 Comments: 1

Let m & n be two positive numbers greater than 1 . If lim_(p→0) ((e^(cos (p^n )) −e)/p^m ) = (1/2)e then (n/m)=?

$$\:\:{Let}\:{m}\:\&\:{n}\:{be}\:{two}\:{positive}\:{numbers}\: \\ $$$$\:{greater}\:{than}\:\mathrm{1}\:.\:{If}\:\underset{{p}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{\mathrm{cos}\:\left({p}^{{n}} \right)} −{e}}{{p}^{{m}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}}{e}\: \\ $$$$\:{then}\:\frac{{n}}{{m}}=? \\ $$

Question Number 162398 Answers: 1 Comments: 0

lim_(x→0) ((∫_0 ^1 (arctan (t+sin x)−arctan t)dt)/(arctan x))=?

$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{arctan}\:\left(\mathrm{t}+\mathrm{sin}\:\mathrm{x}\right)−\mathrm{arctan}\:\mathrm{t}\right)\mathrm{dt}}{\mathrm{arctan}\:\mathrm{x}}=? \\ $$

Question Number 162396 Answers: 1 Comments: 1

Question Number 162395 Answers: 0 Comments: 1

Question Number 162390 Answers: 0 Comments: 0

Question Number 162382 Answers: 2 Comments: 0

Question Number 162377 Answers: 1 Comments: 2

prove that ψ′′ ((1/4) )= −2π^( 3) − 56 ζ (3 )

$$ \\ $$$$\:\:{prove}\:\:{that} \\ $$$$ \\ $$$$\:\:\:\:\:\:\psi''\:\left(\frac{\mathrm{1}}{\mathrm{4}}\:\right)=\:−\mathrm{2}\pi^{\:\mathrm{3}} −\:\mathrm{56}\:\zeta\:\left(\mathrm{3}\:\right) \\ $$$$ \\ $$

Question Number 162374 Answers: 0 Comments: 2

Question Number 162371 Answers: 2 Comments: 0

If x ∈R the maximum value of ((3x^2 +9x+17)/(3x^2 +9x+7)) is ...

$$\:\:{If}\:{x}\:\in\mathbb{R}\:{the}\:{maximum}\:{value}\: \\ $$$$\:{of}\:\frac{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{17}}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{7}}\:{is}\:... \\ $$

Question Number 162368 Answers: 1 Comments: 2

Question Number 162367 Answers: 1 Comments: 0

Let x_1 ,x_2 ,x_3 be the roots of the equation x^3 +3x+5=0 . Then the value of expression (x_1 +(1/x_1 ))(x_2 +(1/x_2 ))(x_3 +(1/x_3 )) is equal to

$$\:\:{Let}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,{x}_{\mathrm{3}} \:{be}\:{the}\:{roots}\:{of}\:{the}\: \\ $$$${equation}\:{x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{5}=\mathrm{0}\:.\:{Then}\:{the} \\ $$$${value}\:{of}\:{expression}\:\left({x}_{\mathrm{1}} +\frac{\mathrm{1}}{{x}_{\mathrm{1}} }\right)\left({x}_{\mathrm{2}} +\frac{\mathrm{1}}{{x}_{\mathrm{2}} }\right)\left({x}_{\mathrm{3}} +\frac{\mathrm{1}}{{x}_{\mathrm{3}} }\right)\:{is} \\ $$$$\:{equal}\:{to} \\ $$

Question Number 162366 Answers: 1 Comments: 0

Given that the solution set of the quadratic inequality ax^2 +bx+c >0 is (2,3). Then the solution set of the inequality cx^2 +bx+a <0 will be

$$\:{Given}\:{that}\:{the}\:{solution}\:{set}\:{of}\:{the}\: \\ $$$$\:{quadratic}\:{inequality}\:{ax}^{\mathrm{2}} +{bx}+{c}\:>\mathrm{0} \\ $$$$\:{is}\:\left(\mathrm{2},\mathrm{3}\right).\:{Then}\:{the}\:{solution}\:{set}\: \\ $$$$\:{of}\:{the}\:{inequality}\:{cx}^{\mathrm{2}} +{bx}+{a}\:<\mathrm{0}\: \\ $$$$\:{will}\:{be}\: \\ $$

Question Number 162365 Answers: 0 Comments: 0

∫_0 ^1 ∫_0 ^1 ∫_0 ^1 ln^2 (x+y+z)dxdydz=?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{ln}^{\mathrm{2}} \left({x}+{y}+{z}\right){dxdydz}=? \\ $$

Question Number 162364 Answers: 2 Comments: 1

lim_(x→0) ((5sin x−sin 3x cos 2x−cos 3x sin 2x)/x^3 ) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5sin}\:{x}−\mathrm{sin}\:\mathrm{3}{x}\:\mathrm{cos}\:\mathrm{2}{x}−\mathrm{cos}\:\mathrm{3}{x}\:\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{3}} }\:=? \\ $$

Question Number 162351 Answers: 1 Comments: 0

how to show f(x)=x^4 +2x^3 +5x^2 −16x−20 in the form of (x^2 +x+a)^2 −4(x+b)^2 .

$$\mathrm{how}\:\mathrm{to}\:\mathrm{show}\: \\ $$$${f}\left({x}\right)={x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} −\mathrm{16}{x}−\mathrm{20}\: \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\left({x}^{\mathrm{2}} +{x}+{a}\right)^{\mathrm{2}} −\mathrm{4}\left({x}+{b}\right)^{\mathrm{2}} . \\ $$

Question Number 162348 Answers: 1 Comments: 4

Question Number 162344 Answers: 1 Comments: 1

Question Number 162338 Answers: 1 Comments: 0

(d^2 y/dx^2 ) - 3((dy/dx)) - 4y = tan(x)log(cos(x))

$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:-\:\mathrm{3}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)\:-\:\mathrm{4y}\:=\:\mathrm{tan}\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{cos}\left(\mathrm{x}\right)\right) \\ $$

Question Number 162336 Answers: 1 Comments: 0

lim_( n→∞) ((1/(1+n^( 3) )) +(( 4)/(8 +n^( 3) )) + (9/(27 +n^( 3) )) +...+(n^( 2) /(2n^( 3) )) )=?

$$ \\ $$$${lim}_{\:{n}\rightarrow\infty} \:\left(\frac{\mathrm{1}}{\mathrm{1}+{n}^{\:\mathrm{3}} }\:+\frac{\:\mathrm{4}}{\mathrm{8}\:+{n}^{\:\mathrm{3}} }\:+\:\frac{\mathrm{9}}{\mathrm{27}\:+{n}^{\:\mathrm{3}} }\:+...+\frac{{n}^{\:\mathrm{2}} }{\mathrm{2}{n}^{\:\mathrm{3}} }\:\right)=? \\ $$$$ \\ $$

Question Number 162326 Answers: 1 Comments: 0

Hello please show it... a ∈ [0 , (π/4)] a ≤tan a ≤ 2a

$${Hello}\:{please}\:{show}\:{it}... \\ $$$$\:{a}\:\in\:\left[\mathrm{0}\:,\:\frac{\pi}{\mathrm{4}}\right]\:\:\:\:\:\:\:\:{a}\:\leqslant{tan}\:{a}\:\leqslant\:\mathrm{2}{a} \\ $$

Question Number 162309 Answers: 1 Comments: 3

Question Number 162305 Answers: 2 Comments: 0

proof that 2^(n+1) >(n+2)sin n

$${proof}\:{that} \\ $$$$\mathrm{2}^{{n}+\mathrm{1}} >\left({n}+\mathrm{2}\right)\mathrm{sin}\:{n} \\ $$

Question Number 162303 Answers: 0 Comments: 0

∫_0 ^1 ∫_0 ^1 ∫_0 ^1 ln^2 (x+y+z)dxdydz=?

Question Number 162280 Answers: 1 Comments: 0

y=x^(sinx) find y′

$${y}={x}^{{sinx}} \\ $$$${find}\:\:{y}' \\ $$

Question Number 162278 Answers: 0 Comments: 0

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