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AllQuestion and Answers: Page 1570

Question Number 45270 Answers: 2 Comments: 1

Question Number 45268 Answers: 0 Comments: 0

Question Number 45259 Answers: 2 Comments: 1

Find distance of point (1,1,1) from the line passing through (2,3,4) & (−1,2,3) ?

$${Find}\:\:{distance}\:{of}\:{point}\:\left(\mathrm{1},\mathrm{1},\mathrm{1}\right)\:{from} \\ $$$${the}\:{line}\:{passing}\:{through}\:\left(\mathrm{2},\mathrm{3},\mathrm{4}\right)\:\& \\ $$$$\left(−\mathrm{1},\mathrm{2},\mathrm{3}\right)\:? \\ $$

Question Number 45264 Answers: 0 Comments: 4

Question Number 45239 Answers: 0 Comments: 0

find the range of the following (i) f(x)=arcsin(x) (ii)f(x)=arccos(x) (iii)f(x)=arctan(x)

Question Number 45240 Answers: 2 Comments: 1

calculate Σ_(n=2) ^∞ ((2n+1)/(n^4 −n^2 ))

$${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{4}} −{n}^{\mathrm{2}} } \\ $$

Question Number 45237 Answers: 1 Comments: 1

calculate Σ_(n=2) ^∞ (1/(n^3 −n))

$${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{3}} −{n}} \\ $$

Question Number 45235 Answers: 0 Comments: 2

let ∣a∣<1 and f(a)=∫_0 ^1 ln(x)ln(1+ax)dx 1) find a explicit form of f(a) 2) calculate g(a) =∫_0 ^1 ((xln(x))/(1+ax))dx 3) calculate ∫_0 ^1 ln(x)ln(2+x)dx 4) calculate ∫_0 ^1 ((xln(x))/(2+x))dx 5) calculate u_n =∫_0 ^1 ((xln(x))/(n+x))dx with n integr and n>1 find nature of the serie Σ u_n

$${let}\:\mid{a}\mid<\mathrm{1}\:{and}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{ax}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xln}\left({x}\right)}{\mathrm{1}+{ax}}{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{2}+{x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xln}\left({x}\right)}{\mathrm{2}+{x}}{dx}\: \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xln}\left({x}\right)}{{n}+{x}}{dx}\:{with}\:{n}\:{integr}\:{and}\:{n}>\mathrm{1} \\ $$$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{u}_{{n}} \\ $$

Question Number 45213 Answers: 3 Comments: 0

Find ∫(√(a^2 −tan^2 x)) dx (with a>0) (related to Q45187)

$${Find}\:\int\sqrt{{a}^{\mathrm{2}} −\mathrm{tan}^{\mathrm{2}} \:{x}}\:{dx}\:\left({with}\:{a}>\mathrm{0}\right) \\ $$$$\left({related}\:{to}\:{Q}\mathrm{45187}\right) \\ $$

Question Number 45211 Answers: 1 Comments: 0

Let A= (((1 3)),((2 5)) ). Find an expression for the enteries of A^n .

$$\mathrm{Let}\:\mathrm{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\mathrm{3}}\\{\mathrm{2}\:\:\:\:\:\mathrm{5}}\end{pmatrix}.\:\mathrm{Find}\:\mathrm{an}\:\mathrm{expression}\: \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{enteries}\:\mathrm{of}\:\mathrm{A}^{\mathrm{n}} . \\ $$

Question Number 45208 Answers: 0 Comments: 1

Question Number 45204 Answers: 0 Comments: 2

Question Number 45201 Answers: 0 Comments: 6

find ∫ (dx/(√(1+x^3 )))

$${find}\:\int\:\:\frac{{dx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }} \\ $$

Question Number 45206 Answers: 0 Comments: 1

Question Number 45205 Answers: 2 Comments: 0

Question Number 45192 Answers: 0 Comments: 0

To the developer, of tinkutara; Sir, since yesterday the app crashes when i go for any page other than the main ′sort by question id page′, please help, my phone is 2G compatible android old version, but the app had been running all nice before yesterday night.

$${To}\:{the}\:{developer},\:{of}\:{tinkutara}; \\ $$$${Sir},\:{since}\:{yesterday}\:{the} \\ $$$${app}\:{crashes}\:{when}\:{i}\:{go}\:{for} \\ $$$${any}\:{page}\:{other}\:{than}\:{the} \\ $$$${main}\:'{sort}\:{by}\:{question}\:{id}\:{page}', \\ $$$${please}\:{help},\:{my}\:{phone}\:{is}\:\mathrm{2}{G} \\ $$$${compatible}\:{android}\:{old}\:{version}, \\ $$$${but}\:{the}\:{app}\:{had}\:{been}\:{running}\:{all} \\ $$$${nice}\:{before}\:{yesterday}\:{night}. \\ $$

Question Number 45187 Answers: 1 Comments: 6