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Question Number 29689 Answers: 1 Comments: 2

find lim_(x→0) ((2/(1+a^x )))^(1/x) =?

$${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{2}}{\mathrm{1}+{a}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} =? \\ $$

Question Number 29680 Answers: 1 Comments: 0

i^(i ) what is iota to power iota

$$\mathrm{i}^{\mathrm{i}\:} \:\:\mathrm{what}\:\mathrm{is}\:\mathrm{iota}\:\mathrm{to}\:\mathrm{power}\:\mathrm{iota} \\ $$

Question Number 29658 Answers: 1 Comments: 0

tanθ+tan2θ+(√3) tanθ.tan2θ=(√3) (0^(o ) ≤θ≤360)

$${tan}\theta+{tan}\mathrm{2}\theta+\sqrt{\mathrm{3}}\:{tan}\theta.{tan}\mathrm{2}\theta=\sqrt{\mathrm{3}}\:\:\:\:\:\left(\mathrm{0}^{{o}\:} \leqslant\theta\leqslant\mathrm{360}\right) \\ $$

Question Number 29648 Answers: 1 Comments: 5

How many arrangements are there of 4 letters chosen from the word COMMUNICATION

$$\mathrm{How}\:\mathrm{many}\:\mathrm{arrangements}\:\mathrm{are} \\ $$$$\mathrm{there}\:\mathrm{of}\:\mathrm{4}\:\mathrm{letters}\:\mathrm{chosen}\:\mathrm{from}\: \\ $$$$\mathrm{the}\:\mathrm{word}\:{COMMUNICATION} \\ $$

Question Number 29647 Answers: 0 Comments: 1

Question Number 29645 Answers: 1 Comments: 0

if the sum of first 5 terms of a G.P. is 155, sum of last 5 terms is 39680,first term is 5 and last term is 20480. find the number of terms of the sequence.

$${if}\:{the}\:{sum}\:{of}\:{first}\:\mathrm{5}\:{terms}\:{of}\:\:{a}\:{G}.{P}.\:{is}\:\mathrm{155},\:{sum}\:{of}\:{last}\:\mathrm{5}\:{terms}\:{is}\:\mathrm{39680},{first}\:{term}\:{is}\:\mathrm{5}\:{and}\:{last}\:{term}\:\:{is}\:\mathrm{20480}.\:{find}\:{the}\:{number}\:{of}\:{terms}\:{of}\:{the}\:{sequence}. \\ $$

Question Number 29646 Answers: 0 Comments: 0

Question Number 29643 Answers: 0 Comments: 0

Question Number 29627 Answers: 1 Comments: 1

Question Number 29633 Answers: 1 Comments: 10

Question Number 29611 Answers: 0 Comments: 4

Question Number 29601 Answers: 0 Comments: 0

Question Number 29607 Answers: 0 Comments: 0

Prove the convergence of each of the following sequence (i) {((n − 1)/n)}_(n = 1) ^∞ (ii) {(1/(2)^(1/n) )}_(n = 1) ^∞ (iii) {((n + 1)/n)}_(n = 1) ^∞

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence} \\ $$$$\left(\mathrm{i}\right)\:\:\left\{\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\right\}_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \:\:\:\:\:\:\:\:\left(\mathrm{ii}\right)\:\:\:\left\{\frac{\mathrm{1}}{\sqrt[{\mathrm{n}}]{\mathrm{2}}}\right\}_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \:\:\:\:\:\:\left(\mathrm{iii}\right)\:\:\:\:\left\{\frac{\mathrm{n}\:+\:\mathrm{1}}{\mathrm{n}}\right\}_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \\ $$

Question Number 29581 Answers: 1 Comments: 0

Let x = 4sin^2 10^o +4sin^2 50^o cos20^o +cos80^o and y = cos^2 (π/5)+cos^2 ((2π)/(15))+cos^2 ((8π)/(15)). find x+y ?

$${Let}\:{x}\:=\:\mathrm{4}{sin}^{\mathrm{2}} \mathrm{10}^{{o}} +\mathrm{4}{sin}^{\mathrm{2}} \mathrm{50}^{{o}} {cos}\mathrm{20}^{{o}} +{cos}\mathrm{80}^{{o}} \\ $$$${and}\:{y}\:=\:{cos}^{\mathrm{2}} \:\frac{\pi}{\mathrm{5}}+{cos}^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{15}}+{cos}^{\mathrm{2}} \frac{\mathrm{8}\pi}{\mathrm{15}}. \\ $$$${find}\:{x}+{y}\:? \\ $$

Question Number 29687 Answers: 1 Comments: 4

Question Number 29592 Answers: 0 Comments: 0

y′=xy^2 +2y+1

$${y}'={xy}^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{1} \\ $$

Question Number 29574 Answers: 0 Comments: 2

∫x^6 −1/x^2 −1dx

$$\int{x}^{\mathrm{6}} −\mathrm{1}/{x}^{\mathrm{2}} −\mathrm{1}{dx} \\ $$

Question Number 29573 Answers: 0 Comments: 2

derive the equation of a chain of length l mass m hanging between two points x distance apart.

$${derive}\:{the}\:{equation}\:{of}\:{a}\:{chain} \\ $$$${of}\:{length}\:{l}\:{mass}\:{m}\:{hanging} \\ $$$${between}\:{two}\:{points}\:{x}\:{distance} \\ $$$${apart}. \\ $$

Question Number 29559 Answers: 1 Comments: 6

Question Number 29554 Answers: 0 Comments: 1

let give f(x)= x^2 cos((1/x^2 )) if x∈]0,1] but its derivative f^′ is not integrable on ]0,1].

$$\left.{l}\left.{et}\:{give}\:{f}\left({x}\right)=\:{x}^{\mathrm{2}} {cos}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\:{if}\:{x}\in\right]\mathrm{0},\mathrm{1}\right]\:{but}\:{its}\:{derivative}\:{f}^{'} \\ $$$$\left.{i}\left.{s}\:{not}\:{integrable}\:{on}\:\right]\mathrm{0},\mathrm{1}\right]. \\ $$

Question Number 29553 Answers: 0 Comments: 0

let put I(x)= ∫_x ^(+∞) ((sin^3 t)/t^2 )dt with x>0 find lim_(x→0^+ ) I(x) 2) find ∫_0 ^∞ ((sin^3 t)/t^2 )dt .

$${let}\:{put}\:\:{I}\left({x}\right)=\:\int_{{x}} ^{+\infty} \:\frac{{sin}^{\mathrm{3}} {t}}{{t}^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$${find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{I}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}^{\mathrm{3}} {t}}{{t}^{\mathrm{2}} }{dt}\:. \\ $$

Question Number 29552 Answers: 1 Comments: 1

find ∫_0 ^∞ (((√(x+1)) −1)/(x(x+1)))dx .

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\sqrt{{x}+\mathrm{1}}\:−\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)}{dx}\:. \\ $$

Question Number 29551 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ ((arctan(2x)−arctanx)/x)dx.

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)−{arctanx}}{{x}}{dx}. \\ $$

Question Number 29550 Answers: 1 Comments: 0

Question Number 29541 Answers: 0 Comments: 4

Question Number 29536 Answers: 1 Comments: 5

Find eccentricity of the ellipse 7x^2 +7y^2 +2xy+10x−10y−7=0 ?

$${Find}\:{eccentricity}\:{of}\:{the}\:{ellipse} \\ $$$$\mathrm{7}{x}^{\mathrm{2}} +\mathrm{7}{y}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{10}{x}−\mathrm{10}{y}−\mathrm{7}=\mathrm{0}\:? \\ $$

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