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Question Number 28770 Answers: 1 Comments: 6

lim_(x→+∞) ((5x^4 −10x^2 +1)/(−3x^3 +10x^2 +50))

$$\underset{{x}\rightarrow+\infty} {{lim}}\:\frac{\mathrm{5}{x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{2}} +\mathrm{1}}{−\mathrm{3}{x}^{\mathrm{3}} +\mathrm{10}{x}^{\mathrm{2}} +\mathrm{50}} \\ $$

Question Number 28762 Answers: 1 Comments: 6

Question Number 28739 Answers: 1 Comments: 0

if S_n =((a(r^n −1))/(r−1)) make r the subject of formula

$${if}\:{S}_{{n}} =\frac{{a}\left({r}^{{n}} −\mathrm{1}\right)}{{r}−\mathrm{1}}\: \\ $$$$ \\ $$$${make}\:{r}\:{the}\:{subject}\:{of}\:{formula} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 28709 Answers: 1 Comments: 0

Question Number 28708 Answers: 0 Comments: 0

If θ = log_e {tan(((3π)/8))} , prove that 3 tanh(2θ) = 2(√2)

$$\mathrm{If}\:\:\:\theta\:\:=\:\:\mathrm{log}_{\mathrm{e}} \left\{\mathrm{tan}\left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\right\}\:,\:\:\:\mathrm{prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\:\mathrm{tanh}\left(\mathrm{2}\theta\right)\:=\:\mathrm{2}\sqrt{\mathrm{2}} \\ $$

Question Number 28706 Answers: 1 Comments: 7

most important question gor boar or iit solve the integration (1/(3sinx+4cosx))

$${most}\:{important}\:{question}\:{gor}\:{boar}\:{or}\:{iit}\: \\ $$$${solve}\:{the}\:{integration}\:\:\frac{\mathrm{1}}{\mathrm{3}{sinx}+\mathrm{4}{cosx}} \\ $$

Question Number 28705 Answers: 1 Comments: 0

solve the integrayion ((sin2x)/(sin5xsin3x))

$${solve}\:{the}\:{integrayion}\:\frac{{sin}\mathrm{2}{x}}{{sin}\mathrm{5}{xsin}\mathrm{3}{x}} \\ $$

Question Number 28703 Answers: 0 Comments: 1

(1/((a^2 +x^2 )^(3/2) )) solve the integration

$$\frac{\mathrm{1}}{\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }\:\:\:{solve}\:{the}\:{integration} \\ $$

Question Number 28702 Answers: 0 Comments: 1

solve integration (1/(√((x−α)(β−x)))) .

$${solve}\:{integration}\:\:\frac{\mathrm{1}}{\sqrt{\left({x}−\alpha\right)\left(\beta−{x}\right)}}\:\:. \\ $$

Question Number 28701 Answers: 1 Comments: 2

integration (x^3 /(x^2 +x+1))

$${integration}\:\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{2}} +{x}+\mathrm{1}} \\ $$

Question Number 28700 Answers: 0 Comments: 0

solve integration (√((sin(x−α))/(sin(x+α))))

$${solve}\:{integration}\:\sqrt{\frac{{sin}\left({x}−\alpha\right)}{{sin}\left({x}+\alpha\right)}} \\ $$

Question Number 28698 Answers: 0 Comments: 3

(∞/(negative number))=? ∞ or −∞ ?

$$\frac{\infty}{\mathrm{negative}\:\mathrm{number}}=? \\ $$$$\:\infty\:\:\:\:\:\:\:\:\:\:\mathrm{or}\:\:\:\:\:\:\:\:\:−\infty\:\:? \\ $$

Question Number 28695 Answers: 1 Comments: 0

∣a^→ +b^→ ∣=40,∣a^→ −b^→ ∣=20&∣a^→ ∣=10 then find∣b^→ ∣

$$\mid\overset{\rightarrow} {\mathrm{a}}+\overset{\rightarrow} {\mathrm{b}}\mid=\mathrm{40},\mid\overset{\rightarrow} {\mathrm{a}}−\overset{\rightarrow} {\mathrm{b}}\mid=\mathrm{20\&}\mid\overset{\rightarrow} {\mathrm{a}}\mid=\mathrm{10}\:\mathrm{then}\:\mathrm{find}\mid\overset{\rightarrow} {\mathrm{b}}\mid \\ $$

Question Number 28694 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ e^(−tx^2 ) cosx dx with t>0 .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{tx}^{\mathrm{2}} } {cosx}\:{dx}\:\:{with}\:{t}>\mathrm{0}\:. \\ $$

Question Number 28690 Answers: 0 Comments: 5

Question Number 28687 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ e^(−( t^2 +(1/t^2 ))) dt.

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left(\:{t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt}. \\ $$

Question Number 28685 Answers: 0 Comments: 0

find the value of I=∫∫_D x^3 dxdy with D= {(x,y)∈R^2 /1≤x≤2 and x^2 −y^2 ≥1 }.

$${find}\:{the}\:{value}\:{of}\:\:{I}=\int\int_{{D}} \:{x}^{\mathrm{3}} {dxdy}\:\:\:{with} \\ $$$${D}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:{and}\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:\:\geqslant\mathrm{1}\:\:\right\}. \\ $$

Question Number 28684 Answers: 0 Comments: 0

find sum of S(x)= Σ_(n=1) ^∞ (−1)^(n−1) (x^(2n+1) /(4n^2 −1)) .

$${find}\:\:{sum}\:{of}\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:. \\ $$

Question Number 28683 Answers: 0 Comments: 1

developp f(x)=e^(−αx) 2π periodic at Fourier serie with α>0.

$${developp}\:{f}\left({x}\right)={e}^{−\alpha{x}} \:\:\:\mathrm{2}\pi\:{periodic}\:{at}\:{Fourier}\:{serie}\:{with} \\ $$$$\alpha>\mathrm{0}. \\ $$

Question Number 28682 Answers: 0 Comments: 2

nature of the serie Σ_(n=0) ^∞ tan(((2n+1)/n^3 )) .

$${nature}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{tan}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{3}} }\right)\:. \\ $$

Question Number 28681 Answers: 0 Comments: 0

give a equivalent of w_n = Σ_(k=n+1) ^∞ (1/(k!)) .

$${give}\:{a}\:{equivalent}\:{of}\:\:{w}_{{n}} =\:\:\:\sum_{{k}={n}+\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{k}!}\:\:. \\ $$

Question Number 28680 Answers: 0 Comments: 0

find lim_(ξ→0) ∫_0 ^(π/2) (dx/(√(sin^2 x +ξcos^2 x))) .

$${find}\:\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{dx}}{\sqrt{{sin}^{\mathrm{2}} {x}\:+\xi{cos}^{\mathrm{2}} {x}}}\:\:\:\:\:. \\ $$

Question Number 28679 Answers: 0 Comments: 1

f function contnue on [0,1] .prove that lim_(n→+∞) n∫_0 ^1 t^n f(t)dt=f(1).

$${f}\:{function}\:{contnue}\:{on}\:\left[\mathrm{0},\mathrm{1}\right]\:.{prove}\:{that} \\ $$$${lim}_{{n}\rightarrow+\infty} \:\:{n}\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{t}^{{n}} {f}\left({t}\right){dt}={f}\left(\mathrm{1}\right). \\ $$

Question Number 28678 Answers: 0 Comments: 0

let give A= (((1 (α/n))),((−(α/n) 1)) ) with n ∈N^∗ and α∈R find lim_(n→+∞) A^n .

$${let}\:{give}\:{A}=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\frac{\alpha}{{n}}}\\{−\frac{\alpha}{{n}}\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$${with}\:{n}\:\in{N}^{\ast} \:\:{and}\:\alpha\in{R}\:\:\:{find}\:\:{lim}_{{n}\rightarrow+\infty} {A}^{{n}} \:\:. \\ $$

Question Number 28677 Answers: 0 Comments: 1

find ∫_0 ^1 ((lnx)/(x−1))dx

$${find}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{lnx}}{{x}−\mathrm{1}}{dx} \\ $$

Question Number 28676 Answers: 0 Comments: 1

let give u_n = ∫_(nπ) ^((n+1)π) e^(−λt) ((sint)/(√t)) with λ>0 calculate Σ_(n=0) ^(+∞) u_n .

$${let}\:{give}\:\:{u}_{{n}} =\:\int_{{n}\pi} ^{\left({n}+\mathrm{1}\right)\pi} \:\:{e}^{−\lambda{t}} \:\frac{{sint}}{\sqrt{{t}}}\:\:\:\:{with}\:\lambda>\mathrm{0} \\ $$$${calculate}\:\sum_{{n}=\mathrm{0}} ^{+\infty} \:\:\:{u}_{{n}} \:.\: \\ $$$$ \\ $$

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