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Question Number 220843 Answers: 0 Comments: 1

α ∈ R lim_(x→1) (((1 − x)^α )/(^3 (√(1 − x^4 )))) ∈(0,∞)

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\alpha\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\mathrm{lim}_{{x}\rightarrow\mathrm{1}} \:\frac{\left(\mathrm{1}\:−\:{x}\right)^{\alpha} }{\:^{\mathrm{3}} \sqrt{\mathrm{1}\:−\:{x}^{\mathrm{4}} }}\:\:\:\:\:\:\:\:\in\left(\mathrm{0},\infty\right) \\ $$$$ \\ $$

Question Number 220842 Answers: 0 Comments: 2

J=∫_0 ^( ∞) e^(−t) u_π (t)cos(t)dt=? note: u_c (t)= { (( 0 t<c)),(( 1 t>c )) :} ; c≥0

$$ \\ $$$$\:\:\:\:\:\:\mathrm{J}=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{t}} {u}_{\pi} \left({t}\right){cos}\left({t}\right){dt}=? \\ $$$$ \\ $$$$\:{note}:\:\:{u}_{{c}} \left({t}\right)=\:\begin{cases}{\:\mathrm{0}\:\:\:\:\:\:\:\:{t}<{c}}\\{\:\mathrm{1}\:\:\:\:\:\:\:\:\:{t}>{c}\:\:}\end{cases}\:\:;\:\:\:\:{c}\geqslant\mathrm{0} \\ $$

Question Number 220830 Answers: 0 Comments: 2

Question Number 220832 Answers: 3 Comments: 0

Question Number 220831 Answers: 1 Comments: 0

Question Number 220825 Answers: 1 Comments: 0

Question Number 220820 Answers: 1 Comments: 1

Question Number 220811 Answers: 0 Comments: 0

Question Number 220810 Answers: 1 Comments: 3

Question Number 220800 Answers: 0 Comments: 0

To Tinkutara [(a),(b) ], determinant ((a),(b)), ((a),(b) ) , { (a),(b) :} , {: (a),(b) } , determinant (((abcdefg)),((pqrstvw))) is work well but invisible line matrix(?) dosen′t work pls Fix bug

$$\mathrm{To}\:\mathrm{Tinkutara} \\ $$$$\begin{bmatrix}{\mathrm{a}}\\{\mathrm{b}}\end{bmatrix},\begin{vmatrix}{\mathrm{a}}\\{\mathrm{b}}\end{vmatrix},\begin{pmatrix}{\mathrm{a}}\\{\mathrm{b}}\end{pmatrix}\:,\begin{cases}{\mathrm{a}}\\{\mathrm{b}}\end{cases}\:,\:\:\left.\begin{matrix}{\mathrm{a}}\\{\mathrm{b}}\end{matrix}\right\}\:,\begin{array}{|c|c|}{\mathrm{abcdefg}}\\{\mathrm{pqrstvw}}\\\hline\end{array}\:\mathrm{is}\:\mathrm{work}\:\mathrm{well} \\ $$$$\mathrm{but}\:\mathrm{invisible}\:\mathrm{line}\:\mathrm{matrix}\left(?\right)\:\mathrm{dosen}'\mathrm{t}\:\mathrm{work} \\ $$$$\mathrm{pls}\:\mathrm{Fix}\:\mathrm{bug} \\ $$

Question Number 220791 Answers: 0 Comments: 0

∫_( 0) ^( 1) (x^2 /(sin x + 1)) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{x}^{\mathrm{2}} }{\boldsymbol{\mathrm{sin}}\:{x}\:+\:\mathrm{1}}\:{dx} \\ $$$$ \\ $$

Question Number 220790 Answers: 1 Comments: 0

Complex integral ∮_( C) (dz/(z^3 +1))=?? , C;x^2 +y^2 =4 ∮_( C) (1/z)e^z dz, C; { ((y=1 , −1≤x≤1)),((y=−1 , −1≤x≤1)),((x=1 , −1≤y≤1)),((x=−1 , −1≤y≤1)) :}

$$\mathrm{Complex}\:\mathrm{integral} \\ $$$$\oint_{\:\mathrm{C}} \:\frac{\mathrm{d}{z}}{{z}^{\mathrm{3}} +\mathrm{1}}=??\:,\:{C};{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4} \\ $$$$\oint_{\:{C}} \:\frac{\mathrm{1}}{{z}}{e}^{{z}} \:\mathrm{d}{z},\:{C};\begin{cases}{{y}=\mathrm{1}\:,\:−\mathrm{1}\leq{x}\leq\mathrm{1}}\\{{y}=−\mathrm{1}\:,\:−\mathrm{1}\leq{x}\leq\mathrm{1}}\\{{x}=\mathrm{1}\:,\:−\mathrm{1}\leq{y}\leq\mathrm{1}}\\{{x}=−\mathrm{1}\:,\:−\mathrm{1}\leq{y}\leq\mathrm{1}}\end{cases}\: \\ $$

Question Number 220770 Answers: 1 Comments: 0

∫_0 ^( (π/2)) (( sin(x))/( (√(1 +(√(sin(2x)))))))dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{sin}\left({x}\right)}{\:\sqrt{\mathrm{1}\:+\sqrt{{sin}\left(\mathrm{2}{x}\right)}}}{dx}\: \\ $$

Question Number 220769 Answers: 2 Comments: 0