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AllQuestion and Answers: Page 1227

Question Number 82398 Answers: 0 Comments: 0

Question Number 82397 Answers: 0 Comments: 2

Question Number 82392 Answers: 0 Comments: 2

Question Number 82391 Answers: 0 Comments: 1

∫ sin x cos (sin x) dx ?

$$\int\:\mathrm{sin}\:{x}\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\:{dx}\:? \\ $$

Question Number 82387 Answers: 0 Comments: 0

Question Number 82386 Answers: 0 Comments: 0

Question Number 82378 Answers: 1 Comments: 1

Question Number 82375 Answers: 2 Comments: 0

if x+y=8 ,,x,y∈R^+ prove that (x+(1/y))^2 +(y+(1/x))^2 ≥((289)/8)

$${if}\:\:{x}+{y}=\mathrm{8}\:\:\:\:\:,,{x},{y}\in\mathbb{R}^{+} \\ $$$${prove}\:{that}\: \\ $$$$\left({x}+\frac{\mathrm{1}}{{y}}\right)^{\mathrm{2}} +\left({y}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} \geqslant\frac{\mathrm{289}}{\mathrm{8}} \\ $$

Question Number 82365 Answers: 0 Comments: 3

Question Number 82358 Answers: 0 Comments: 3

Show that: a_n = − rω^2 , show clearly how you arrive at your result.

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\:\mathrm{a}_{\mathrm{n}} \:\:=\:\:−\:\mathrm{r}\omega^{\mathrm{2}} \:,\:\:\:\mathrm{show}\:\mathrm{clearly}\:\mathrm{how}\:\mathrm{you}\:\mathrm{arrive} \\ $$$$\mathrm{at}\:\mathrm{your}\:\mathrm{result}. \\ $$

Question Number 82356 Answers: 0 Comments: 1

Question Number 82350 Answers: 0 Comments: 1

2y′′ +5y′ −3y=0 general and particular solution when x =0 , y = 4 and (dy/dx) = 9?

$$\mathrm{2}{y}''\:+\mathrm{5}{y}'\:−\mathrm{3}{y}=\mathrm{0} \\ $$$${general}\:{and}\:{particular}\:{solution} \\ $$$${when}\:{x}\:=\mathrm{0}\:,\:{y}\:=\:\mathrm{4}\:{and}\:\frac{{dy}}{{dx}}\:=\:\mathrm{9}? \\ $$

Question Number 82349 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (1/(n^2 +1))=?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{1}}=? \\ $$

Question Number 82339 Answers: 0 Comments: 1

Question Number 82658 Answers: 1 Comments: 2

coefficient x^6 from expressi (2x+1)^(6 ) × (x^2 +x+(1/4))^4 ?

$${coefficient}\:{x}^{\mathrm{6}} \:{from}\:{expressi}\: \\ $$$$\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{6}\:} ×\:\left({x}^{\mathrm{2}} +{x}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} \:? \\ $$

Question Number 82333 Answers: 0 Comments: 0

(y^4 −2xy) dx = −3x^2 dy

$$\left({y}^{\mathrm{4}} −\mathrm{2}{xy}\right)\:{dx}\:=\:−\mathrm{3}{x}^{\mathrm{2}} \:{dy} \\ $$

Question Number 82330 Answers: 0 Comments: 4

Question Number 82308 Answers: 0 Comments: 1

Question Number 82307 Answers: 0 Comments: 3

Question Number 82303 Answers: 0 Comments: 18

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Question Number 82290 Answers: 0 Comments: 0

calculate Σ_(p≥2 and q≥2) (1/p^q )

$${calculate}\:\sum_{{p}\geqslant\mathrm{2}\:{and}\:{q}\geqslant\mathrm{2}} \:\:\frac{\mathrm{1}}{{p}^{{q}} } \\ $$

Question Number 82289 Answers: 1 Comments: 4

calculate Σ_(n=6) ^∞ (1/(n^2 −25))

$${calculate}\:\sum_{{n}=\mathrm{6}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} −\mathrm{25}} \\ $$

Question Number 82288 Answers: 0 Comments: 0

calculate lim_(n→+∞) (1+(1/n))^n^2 ((n!)/n^(n+(1/2)) )

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}^{\mathrm{2}} } \frac{{n}!}{{n}^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$

Question Number 82287 Answers: 0 Comments: 0

find nature of the serie Σ (n^n /(n! e^n ))

$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:\frac{{n}^{{n}} }{{n}!\:{e}^{{n}} } \\ $$

Question Number 82286 Answers: 1 Comments: 3

1) find a and b wich verify ∫_0 ^π (at^2 +bt)cos(nx) =(1/n^2 ) 2) find the value of Σ_(n=1) ^∞ (1/n^2 )

$$\left.\mathrm{1}\right)\:{find}\:{a}\:{and}\:{b}\:{wich}\:{verify}\:\:\int_{\mathrm{0}} ^{\pi} \left({at}^{\mathrm{2}} \:+{bt}\right){cos}\left({nx}\right)\:=\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$

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