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Question Number 160263 Answers: 1 Comments: 1

Σ_(r=0) ^∞ ((sin(rα))/(r!))

$$\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{sin}\left({r}\alpha\right)}{{r}!} \\ $$

Question Number 160259 Answers: 0 Comments: 0

Find: Σ_(n=1) ^∞ (-1)^(n+1) ((1∙4∙...∙(3n-2))/(7∙9∙...∙(2n+5))) = ?

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\left(-\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:\frac{\mathrm{1}\centerdot\mathrm{4}\centerdot...\centerdot\left(\mathrm{3n}-\mathrm{2}\right)}{\mathrm{7}\centerdot\mathrm{9}\centerdot...\centerdot\left(\mathrm{2n}+\mathrm{5}\right)}\:=\:? \\ $$

Question Number 160256 Answers: 0 Comments: 2

lim_(x→2) ((sin x^x −sin 2^x )/(2^x^x −2^2^x ))=?

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

Question Number 160254 Answers: 1 Comments: 0

Question Number 160253 Answers: 0 Comments: 0

Question Number 160252 Answers: 2 Comments: 0

∫_0 ^( 1) (( ln^( 2) (1−x )ln(x))/x)dx=?

$$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}\:\right){ln}\left({x}\right)}{{x}}{dx}=? \\ $$$$ \\ $$

Question Number 160296 Answers: 1 Comments: 1

Question Number 160246 Answers: 1 Comments: 0

Question Number 160244 Answers: 1 Comments: 0

Li_(x→0) m (((tan^(−1) (x)−tan (x))/(sin^(−1) (x)−sin (x))))=?

$$\:\:\:\:\:{L}\underset{{x}\rightarrow\mathrm{0}} {{i}m}\:\left(\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)−\mathrm{tan}\:\left({x}\right)}{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)−\mathrm{sin}\:\left({x}\right)}\right)=? \\ $$

Question Number 160241 Answers: 1 Comments: 1

Question Number 160233 Answers: 0 Comments: 0

Question Number 160235 Answers: 2 Comments: 0

solve 3^x +3x=10

$${solve}\:\mathrm{3}^{{x}} +\mathrm{3}{x}=\mathrm{10} \\ $$

Question Number 160223 Answers: 0 Comments: 0

Ω:=∫_0 ^( ∞) (( x)/(( e^( x) +e^( −x) )^( 3) )) dx =?

$$ \\ $$$$\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}}{\left(\:{e}^{\:{x}} \:+{e}^{\:−{x}} \right)^{\:\mathrm{3}} }\:{dx}\:=? \\ $$

Question Number 160219 Answers: 0 Comments: 0

Σ_(k=1) ^n Π_(i=1) ^m (i^2 −k)k^4 how to solving is programming C++

$$\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{{n}} {\sum}}\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{{m}} {\prod}}\left(\boldsymbol{{i}}^{\mathrm{2}} −\boldsymbol{{k}}\right)\boldsymbol{{k}}^{\mathrm{4}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{{solving}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{programming}}\:\:\boldsymbol{\mathrm{C}}++ \\ $$

Question Number 160215 Answers: 0 Comments: 0

Question Number 160221 Answers: 1 Comments: 4

Question Number 160204 Answers: 1 Comments: 1

∫_0 ^1 (x/(1−x^3 ))=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{3}} }=? \\ $$

Question Number 160205 Answers: 3 Comments: 0

Question Number 160194 Answers: 1 Comments: 1

∫_0 ^1 (x/(1−x^6 ))dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{6}} }\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 160218 Answers: 1 Comments: 0

lim_(x→+∞) ((∫_0 ^x (arctan t)^2 dt)/( (√(1+x^2 ))))=?

$$\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{arctan}\:\mathrm{t}\right)^{\mathrm{2}} \mathrm{dt}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}=? \\ $$

Question Number 160191 Answers: 1 Comments: 0

∫_1 ^( 2) ∫_0 ^( π) y sin(xy) dy dx

$$\int_{\mathrm{1}} ^{\:\mathrm{2}} \:\int_{\mathrm{0}} ^{\:\pi} \:{y}\:{sin}\left({xy}\right)\:{dy}\:{dx} \\ $$

Question Number 160190 Answers: 3 Comments: 0

if a = (4)^(1/3) + (2)^(1/3) + 1 find (3/a) + (3/a^2 ) + (1/a^3 ) = ?

$$\mathrm{if}\:\:\:\mathrm{a}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{4}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{2}}\:+\:\mathrm{1} \\ $$$$\mathrm{find}\:\:\:\frac{\mathrm{3}}{\mathrm{a}}\:+\:\frac{\mathrm{3}}{\mathrm{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 160188 Answers: 0 Comments: 1

Question Number 160179 Answers: 1 Comments: 2

5^(2(x−2)) (5^(2(x−1)) )^((x+1)) > 125^(x−1)

$$\:\mathrm{5}^{\mathrm{2}\left({x}−\mathrm{2}\right)} \left(\mathrm{5}^{\mathrm{2}\left({x}−\mathrm{1}\right)} \right)^{\left({x}+\mathrm{1}\right)} \:>\:\mathrm{125}^{{x}−\mathrm{1}} \\ $$

Question Number 160171 Answers: 0 Comments: 0

Question Number 160170 Answers: 0 Comments: 0

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