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... advanced mathematcs ... prove that:: Σ_(n=1) ^∞ (((−1)^n )/(1+n^2 )) =((csch(π)−1)/2)

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\:\:{advanced}\:\:{mathematcs}\:\:... \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{1}+{n}^{\mathrm{2}} }\:=\frac{{csch}\left(\pi\right)−\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$

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Question Number 129804 Answers: 1 Comments: 0

If p^→ =2i^ +5j^ +6k^ q^→ =3i^ +6j^ +8k^ r^→ =2i^ +6j^ +10k^ find p^→ ×q^→ ×r^→ ?

$$\mathrm{If}\:\overset{\rightarrow} {{p}}=\mathrm{2}\hat {{i}}+\mathrm{5}\hat {{j}}+\mathrm{6}\hat {{k}} \\ $$$$\:\:\:\overset{\rightarrow} {{q}}=\mathrm{3}\hat {{i}}+\mathrm{6}\hat {{j}}+\mathrm{8}\hat {{k}} \\ $$$$\:\:\:\overset{\rightarrow} {{r}}=\mathrm{2}\hat {{i}}+\mathrm{6}\hat {{j}}+\mathrm{10}\hat {{k}}\: \\ $$$$\:\mathrm{find}\:\overset{\rightarrow} {{p}}×\overset{\rightarrow} {{q}}×\overset{\rightarrow} {{r}}\:? \\ $$

Question Number 128830 Answers: 2 Comments: 0

Question Number 128347 Answers: 0 Comments: 0

E is a vectorial space wich has as base (i^→ ,j^→ ,k^→ ). P={ ((x),(y),(( z)) ) such that 5x+y+z=0} 1. Determinate one base of P.

$${E}\:{is}\:{a}\:{vectorial}\:{space}\:{wich}\:{has}\:{as}\:{base}\: \\ $$$$\left(\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}},\overset{\rightarrow} {{k}}\right).\: \\ $$$${P}=\left\{\begin{pmatrix}{{x}}\\{{y}}\\{\:{z}}\end{pmatrix}\:{such}\:{that}\:\mathrm{5}{x}+{y}+{z}=\mathrm{0}\right\} \\ $$$$\mathrm{1}.\:{Determinate}\:{one}\:{base}\:{of}\:{P}. \\ $$

Question Number 128314 Answers: 2 Comments: 0

∫_0 ^( ∞) ((sin(px))/( (√x))) dx ∀p∈R

$$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\mathrm{px}\right)}{\:\sqrt{\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\forall\mathrm{p}\in\mathbb{R} \\ $$

Question Number 128245 Answers: 1 Comments: 0

nice calculus... prove that :: ∫_0 ^( (π/4)) xcot(x)dx=(1/2)(G+(π/4)log(2))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:\:{calculus}... \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\:::\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {xcot}\left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\left({G}+\frac{\pi}{\mathrm{4}}{log}\left(\mathrm{2}\right)\right) \\ $$

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maximum value of direction derivative of Φ:e^(3x) sin(yz^4 )at(0 ,π/4, 1) is?

$${maximum}\:{value}\:{of}\:{direction}\:{derivative}\:{of}\:\Phi:{e}^{\mathrm{3}{x}} {sin}\left({yz}^{\mathrm{4}} \right){at}\left(\mathrm{0}\:\:,\pi/\mathrm{4},\:\:\mathrm{1}\right)\:{is}? \\ $$

Question Number 126414 Answers: 1 Comments: 0

Question Number 126398 Answers: 0 Comments: 0

r^→ (t)=4sin^2 ti^→ +4cos^2 tj^→ −3k^→

$$\overset{\rightarrow} {\mathrm{r}}\left(\mathrm{t}\right)=\mathrm{4sin}^{\mathrm{2}} \mathrm{t}\overset{\rightarrow} {\mathrm{i}}+\mathrm{4cos}^{\mathrm{2}} \mathrm{t}\overset{\rightarrow} {\mathrm{j}}−\mathrm{3}\overset{\rightarrow} {\mathrm{k}} \\ $$

Question Number 125662 Answers: 1 Comments: 0

I = ∫_0 ^4 tanh^(−1) 2x dx = ???

$$\:\mathcal{I}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\mathrm{tanh}^{−\mathrm{1}} \:\mathrm{2}{x}\:{dx}\:=\:??? \\ $$

Question Number 124131 Answers: 1 Comments: 0

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