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Question Number 163675    Answers: 0   Comments: 1

how do we find the sum of the terms after the n^(th) term of a GP

$${how}\:{do}\:{we}\:{find}\:{the}\:{sum}\:{of}\:{the}\:{terms}\:{after}\: \\ $$$${the}\:{n}^{{th}} \:{term}\:{of}\:{a}\:{GP} \\ $$

Question Number 163666    Answers: 4   Comments: 0

lim _(x→𝛑) (((x^𝛑 βˆ’ 𝛑^x )/(xβˆ’π›‘))) =?? β‰ͺzaynal≫

$$\boldsymbol{\mathrm{lim}}\:_{\boldsymbol{{x}}\rightarrow\boldsymbol{\pi}} \:\:\left(\frac{\boldsymbol{{x}}^{\boldsymbol{\pi}} \:βˆ’\:\boldsymbol{\pi}^{\boldsymbol{{x}}} }{\boldsymbol{{x}}βˆ’\boldsymbol{\pi}}\right)\:=?? \\ $$$$\ll\mathrm{zaynal}\gg \\ $$

Question Number 163662    Answers: 1   Comments: 1

Question Number 163651    Answers: 1   Comments: 1

if (aβˆ’2b)^2 +(bβˆ’2c)^2 =0 find volve (((b+cβˆ’a)^3 )/(abc))=?

$${if}\:\:\left({a}βˆ’\mathrm{2}{b}\right)^{\mathrm{2}} +\left({b}βˆ’\mathrm{2}{c}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:\:{volve}\:\:\frac{\left({b}+{c}βˆ’{a}\right)^{\mathrm{3}} }{{abc}}=? \\ $$

Question Number 163650    Answers: 1   Comments: 2

lim_(xβ†’Ο€) ((x^Ο€^x βˆ’Ο€^x^Ο€ )/(xβˆ’Ο€))=?

$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{{x}^{\pi^{{x}} } βˆ’\pi^{{x}^{\pi} } }{{x}βˆ’\pi}=? \\ $$

Question Number 163642    Answers: 1   Comments: 0

lim_(xβ†’(2/3)) ((⌊3xβŒ‹βˆ’3x)/(9x^2 βˆ’4)) =?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\frac{\mathrm{2}}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\lfloor\mathrm{3}{x}\rfloorβˆ’\mathrm{3}{x}}{\mathrm{9}{x}^{\mathrm{2}} βˆ’\mathrm{4}}\:=? \\ $$

Question Number 163638    Answers: 0   Comments: 2

∫ (dx/( (√(2c_1 +e^(βˆ’2x) ))))

$$\int\:\frac{\boldsymbol{{dx}}}{\:\sqrt{\mathrm{2}\boldsymbol{{c}}_{\mathrm{1}} +\boldsymbol{{e}}^{βˆ’\mathrm{2}\boldsymbol{{x}}} }} \\ $$

Question Number 163632    Answers: 2   Comments: 0

(((x^2 - y^2 )βˆ™(√3))/( (√(x^3 + 3x^2 y + 3xy^2 + y^3 )))) = -1 x^3 + y^3 = (x + y)^2 find: x and y

$$\frac{\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{y}^{\mathrm{2}} \right)\centerdot\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \mathrm{y}\:+\:\mathrm{3xy}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{3}} }}\:=\:-\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\left(\mathrm{x}\:+\:\mathrm{y}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}} \\ $$

Question Number 163631    Answers: 2   Comments: 0

x + (1/x) = (√3) β‡’ x^(3579) + (1/x^(3579) ) = ?

$$\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\sqrt{\mathrm{3}}\:\:\Rightarrow\:\mathrm{x}^{\mathrm{3579}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3579}} }\:=\:? \\ $$

Question Number 163627    Answers: 2   Comments: 0

Question Number 163624    Answers: 1   Comments: 0

Question Number 163619    Answers: 1   Comments: 2

Prove that; ∫_(βˆ’βˆž) ^0 e^(βˆ’βˆ£t∣) dt = 1

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}}; \\ $$$$\:\:\int_{βˆ’\infty} ^{\mathrm{0}} \:\boldsymbol{{e}}^{βˆ’\mid\boldsymbol{{t}}\mid} \:\boldsymbol{{dt}}\:=\:\mathrm{1} \\ $$

Question Number 163618    Answers: 0   Comments: 0

Question Number 163613    Answers: 0   Comments: 0

Question Number 163614    Answers: 0   Comments: 0

∫((sec^2 x)/((secx+tanx)^(9/2) ))dx

$$\int\frac{{sec}^{\mathrm{2}} {x}}{\left({secx}+{tanx}\right)^{\mathrm{9}/\mathrm{2}} }{dx} \\ $$

Question Number 163611    Answers: 1   Comments: 0

Question Number 163610    Answers: 1   Comments: 0

Question Number 163609    Answers: 0   Comments: 0

lim_(nβ†’βˆž) n[Aβˆ’n(H_n βˆ’lnnβˆ’Ξ³)]=B Find (A/B)=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}\left[\mathrm{A}βˆ’\mathrm{n}\left(\mathrm{H}_{\mathrm{n}} βˆ’\mathrm{lnn}βˆ’\gamma\right)\right]=\mathrm{B} \\ $$$$\mathrm{Find}\:\frac{\mathrm{A}}{\mathrm{B}}=? \\ $$

Question Number 163608    Answers: 0   Comments: 0

A_n =(n/(n^2 +1^2 ))+(n/(n^2 +2^2 ))+...+(n/(n^2 +n^2 )) Prove:: lim_(nβ†’βˆž) (1/(n^4 {(1/(24))βˆ’n[n((Ο€/4)βˆ’A_n )βˆ’(1/4)]}))=2016

$$\mathrm{A}_{\mathrm{n}} =\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }+...+\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} } \\ $$$$\mathrm{Prove}::\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{4}} \left\{\frac{\mathrm{1}}{\mathrm{24}}βˆ’\mathrm{n}\left[\mathrm{n}\left(\frac{\pi}{\mathrm{4}}βˆ’\mathrm{A}_{\mathrm{n}} \right)βˆ’\frac{\mathrm{1}}{\mathrm{4}}\right]\right\}}=\mathrm{2016} \\ $$

Question Number 163601    Answers: 0   Comments: 0

∫_(2/Ο€) ^(+oo) ln(cos((1/x)))dx narure?

$$\int_{\frac{\mathrm{2}}{\pi}} ^{+{oo}} {ln}\left({cos}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$$${narure}? \\ $$

Question Number 163600    Answers: 1   Comments: 0

a line charges of charge density pl=4x^3 βˆ’x+3mc/m laying along the xβˆ’axis. determine the total charge if the line charge extends from x=2 and x=6 m

$${a}\:{line}\:{charges}\:{of}\:{charge}\:{density}\: \\ $$$${pl}=\mathrm{4}{x}^{\mathrm{3}} βˆ’{x}+\mathrm{3}{mc}/{m}\:{laying}\:{along}\:{the}\:{x}βˆ’{axis}. \\ $$$${determine}\:{the}\:{total}\:{charge}\:{if}\:{the}\:{line}\:{charge} \\ $$$${extends}\:{from}\:{x}=\mathrm{2}\:{and}\:{x}=\mathrm{6}\:{m} \\ $$

Question Number 163591    Answers: 0   Comments: 3

Re^ soudre (βˆ‚^2 u/βˆ‚x^2 )+(βˆ‚^2 u/βˆ‚y^2 )=10e^(2x+y)

$$\mathrm{R}\acute {\mathrm{e}soudre}\:\:\:\:\:\:\frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {u}}{\partial{y}^{\mathrm{2}} }=\mathrm{10}{e}^{\mathrm{2}{x}+{y}} \\ $$

Question Number 163586    Answers: 0   Comments: 0

Question Number 163587    Answers: 1   Comments: 0

Question Number 163588    Answers: 0   Comments: 0

In β–³ABC prove that (a/b) + (b/c) + (c/a) + (R^2 /(4r^2 )) β‰₯ 1 + (b^2 /a^2 ) + (c^2 /b^2 ) + (a^2 /c^2 )

$${In}\:\:\bigtriangleup{ABC}\:\:{prove}\:{that} \\ $$$$\frac{{a}}{{b}}\:+\:\frac{{b}}{{c}}\:+\:\frac{{c}}{{a}}\:+\:\frac{{R}^{\mathrm{2}} }{\mathrm{4}{r}^{\mathrm{2}} }\:\geqslant\:\mathrm{1}\:+\:\frac{{b}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:\frac{{c}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:+\:\frac{{a}^{\mathrm{2}} }{{c}^{\mathrm{2}} } \\ $$

Question Number 163582    Answers: 1   Comments: 0

lim_(xβ†’βˆž) ((7^(x+2) +6^x )/(3^(2x) βˆ’5^x ))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{7}^{{x}+\mathrm{2}} +\mathrm{6}^{{x}} }{\mathrm{3}^{\mathrm{2}{x}} βˆ’\mathrm{5}^{{x}} }=? \\ $$

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