Question and Answers Forum

AllQuestion and Answers: Page 235

Question Number 197906 Answers: 1 Comments: 0

S= Σ_(k=1) ^∞ (( Γ^( 2) ( k ))/(k Γ (2k ))) = ? −−−−

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{S}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\Gamma^{\:\mathrm{2}} \left(\:{k}\:\right)}{{k}\:\Gamma\:\left(\mathrm{2}{k}\:\right)}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:−−−− \\ $$

Question Number 197795 Answers: 2 Comments: 0

Question Number 197794 Answers: 1 Comments: 0

if x = log tan((π/4)+(y/2)), prove that y = −ilog tan(((ix)/2) + (π/4)) here i = (√(−1))

$$\:\:\:\:\mathrm{if}\:\mathrm{x}\:\:\:=\:\:\:\mathrm{log}\:\mathrm{tan}\left(\frac{\pi}{\mathrm{4}}+\frac{\mathrm{y}}{\mathrm{2}}\right),\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\mathrm{y}\:\:\:\:=\:\:\:−{i}\mathrm{log}\:\mathrm{tan}\left(\frac{{ix}}{\mathrm{2}}\:+\:\frac{\pi}{\mathrm{4}}\right)\:\:\:\:\:\mathrm{here}\:{i}\:\:=\:\sqrt{−\mathrm{1}} \\ $$

Question Number 197792 Answers: 2 Comments: 0

Solve the following differential equation 1) y′′ + y = e^x + x^3 , y(0)=2, y′(0)=0 2) y′′ + y^′ − 2y = x + sin2x, y(0)=1, y′(0)=0 3) y′′ − y′ = xe^x , y(0)=2, y′(0)= 1 Thank you

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{y}''\:+\:\mathrm{y}\:=\:\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{x}^{\mathrm{3}} ,\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{y}''\:+\:\mathrm{y}^{'} \:−\:\mathrm{2y}\:=\:\mathrm{x}\:+\:\mathrm{sin2x},\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1},\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{y}''\:−\:\mathrm{y}'\:=\:\mathrm{xe}^{\mathrm{x}} ,\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{y}'\left(\mathrm{0}\right)=\:\mathrm{1} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 197784 Answers: 1 Comments: 0

((x−2+3((x−3))^(1/3) (1+((x−3))^(1/3) )))^(1/3) + ((x+5+6((x−3))^(1/3) (1+2((x−3))^(1/3) )))^(1/3) = 5

$$\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}+\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\:\left(\mathrm{1}+\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\right)}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}+\mathrm{5}+\mathrm{6}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\left(\mathrm{1}+\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\:\right)}\:=\:\mathrm{5} \\ $$

Question Number 197783 Answers: 2 Comments: 0

∫((x.arctg(x))/(x^2 +1))dx=?

$$\int\frac{{x}.\boldsymbol{{arctg}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}\boldsymbol{{dx}}=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 197776 Answers: 1 Comments: 3

Question Number 197772 Answers: 2 Comments: 1

Can anyone do this? ∫^( +∞) _( 1) ((t−1)/((1+t)^3 lnt))dt

$$\mathrm{Can}\:\mathrm{anyone}\:\mathrm{do}\:\mathrm{this}? \\ $$$$\underset{\:\mathrm{1}} {\int}^{\:+\infty} \frac{\mathrm{t}−\mathrm{1}}{\left(\mathrm{1}+\mathrm{t}\right)^{\mathrm{3}} \:\mathrm{lnt}}\mathrm{dt} \\ $$

Question Number 197771 Answers: 1 Comments: 0

Question Number 197767 Answers: 0 Comments: 1

Question Number 197766 Answers: 1 Comments: 1

∫_0 ^(π/2) (lim_(n→∞) nsin^(2n+1) x cos x)dx = ?

$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}\mathrm{sin}^{\mathrm{2}{n}+\mathrm{1}} {x}\:\mathrm{cos}\:{x}\right){dx}\:\:=\:? \\ $$

Question Number 197763 Answers: 0 Comments: 0

Question Number 197753 Answers: 3 Comments: 0

Solve the equation: (√(5x^2 +14x+9))−(√(x^2 −x−20))=5(√(x+1))

$${Solve}\:{the}\:{equation}: \\ $$$$\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{14}{x}+\mathrm{9}}−\sqrt{{x}^{\mathrm{2}} −{x}−\mathrm{20}}=\mathrm{5}\sqrt{{x}+\mathrm{1}} \\ $$

Question Number 197752 Answers: 1 Comments: 0

find minimum value of m such that m^(19) = 1800 (mod 2029)

$$\:\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m} \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{m}^{\mathrm{19}} =\:\mathrm{1800}\:\left(\mathrm{mod}\:\mathrm{2029}\right) \\ $$

Question Number 197744 Answers: 1 Comments: 0

2∫_0 ^1 tan^(−1) x dx=?

$$\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} {x}\:{dx}=? \\ $$

Question Number 197740 Answers: 3 Comments: 0

Question Number 197734 Answers: 1 Comments: 0

calcul ∫(lnx)^(√x) dx help pls

$$\boldsymbol{{c}}{alcul}\:\int\left(\boldsymbol{{lnx}}\right)^{\sqrt{\boldsymbol{{x}}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{help}}\:\:\boldsymbol{{pls}} \\ $$

Question Number 197730 Answers: 2 Comments: 3

Question Number 197719 Answers: 0 Comments: 3

Determiner x

$$\mathrm{Determiner}\:\:\:\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 197717 Answers: 0 Comments: 5

∡A=62 ∡C=43 Determiner: a=∡B c=∡D b=∡F

$$\measuredangle\boldsymbol{\mathrm{A}}=\mathrm{62}\:\:\:\measuredangle\boldsymbol{\mathrm{C}}=\mathrm{43} \\ $$$$\boldsymbol{\mathrm{Determiner}}:\:\:\mathrm{a}=\measuredangle\boldsymbol{\mathrm{B}}\:\:\:\:\mathrm{c}=\measuredangle\boldsymbol{\mathrm{D}}\:\:\:\:\:\mathrm{b}=\measuredangle\boldsymbol{\mathrm{F}} \\ $$

Question Number 197716 Answers: 0 Comments: 0

sen(x)y^(′′) +cos(x)y′+3x^3 y=tan((√x))

$${sen}\left({x}\right){y}^{''} +{cos}\left({x}\right){y}'+\mathrm{3}{x}^{\mathrm{3}} {y}={tan}\left(\sqrt{{x}}\right) \\ $$

Question Number 197708 Answers: 1 Comments: 0

x^a =x^(a+4) where a∈Z solve for x by showing steps

$$ \\ $$$${x}^{{a}} ={x}^{{a}+\mathrm{4}} \:\:\mathrm{where}\:{a}\in\mathbb{Z} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{x}\:\mathrm{by}\:\mathrm{showing}\:\mathrm{steps} \\ $$

Question Number 197706 Answers: 1 Comments: 0

Question Number 197683 Answers: 2 Comments: 1

((a+3b)/(a+b−1))+((a+3b−1)/(a+b−3))=4 a+b=?

$$\frac{{a}+\mathrm{3}{b}}{{a}+{b}−\mathrm{1}}+\frac{{a}+\mathrm{3}{b}−\mathrm{1}}{{a}+{b}−\mathrm{3}}=\mathrm{4} \\ $$$${a}+{b}=? \\ $$

Question Number 197680 Answers: 1 Comments: 1

Question Number 197667 Answers: 1 Comments: 0

Pg 230 Pg 231 Pg 232 Pg 233 Pg 234 Pg 235 Pg 236 Pg 237 Pg 238 Pg 239

Contact: info@tinkutara.com