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Question Number 61510 Answers: 0 Comments: 0

S_1 =Σ_(k=1) ^n (√((16n−16k)(16n+16k))) S_2 =Σ_(k=1) ^n (√((16k−16)(16k+16))) lim_(n→∞) ((S_1 +S_2 )/n^2 )=?

$${S}_{\mathrm{1}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\sqrt{\left(\mathrm{16}{n}−\mathrm{16}{k}\right)\left(\mathrm{16}{n}+\mathrm{16}{k}\right)} \\ $$$${S}_{\mathrm{2}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\sqrt{\left(\mathrm{16}{k}−\mathrm{16}\right)\left(\mathrm{16}{k}+\mathrm{16}\right)} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{S}_{\mathrm{1}} +{S}_{\mathrm{2}} }{{n}^{\mathrm{2}} }=? \\ $$

Question Number 61402 Answers: 0 Comments: 0

Question Number 61378 Answers: 0 Comments: 0

Solve the differential equation: (dy/dx) = x^2 + y^2

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 61327 Answers: 1 Comments: 0

Question Number 61318 Answers: 1 Comments: 0

Question Number 61241 Answers: 5 Comments: 0

Question Number 61210 Answers: 2 Comments: 1

for what value of θ, e^(iθ) =0

$${for}\:{what}\:{value}\:{of}\:\theta,\:\:{e}^{{i}\theta} =\mathrm{0}\:\: \\ $$

Question Number 61165 Answers: 1 Comments: 0

Question Number 61147 Answers: 1 Comments: 0

prove ∫((1+cos x)/(1−cos x))dx=−2cot (x/2)−x+c

$$\boldsymbol{{prove}} \\ $$$$\int\frac{\mathrm{1}+{cos}\:{x}}{\mathrm{1}−{cos}\:{x}}{dx}=−\mathrm{2}{cot}\:\frac{{x}}{\mathrm{2}}−{x}+{c} \\ $$$$ \\ $$

Question Number 61003 Answers: 3 Comments: 0

Question Number 60984 Answers: 2 Comments: 9

(a/(a−b)) + (b/(b−c)) + (c/(c−a)) = 4 ab^2 + bc^2 + abc + ca^2 = a^2 b + b^2 c + c^2 a ((a/(a−b)))^3 + ((b/(b−c)))^3 + ((c/(c−a)))^3 = ?

$$\frac{{a}}{{a}−{b}}\:\:+\:\:\frac{{b}}{{b}−{c}}\:\:+\:\:\frac{{c}}{{c}−{a}}\:\:=\:\:\mathrm{4} \\ $$$${ab}^{\mathrm{2}} \:+\:{bc}^{\mathrm{2}} \:+\:{abc}\:+\:{ca}^{\mathrm{2}} \:\:=\:\:{a}^{\mathrm{2}} {b}\:+\:{b}^{\mathrm{2}} {c}\:+\:{c}^{\mathrm{2}} {a} \\ $$$$\left(\frac{{a}}{{a}−{b}}\right)^{\mathrm{3}} \:\:+\:\:\left(\frac{{b}}{{b}−{c}}\right)^{\mathrm{3}} \:\:+\:\:\left(\frac{{c}}{{c}−{a}}\right)^{\mathrm{3}} \:\:=\:\:? \\ $$$$ \\ $$

Question Number 60955 Answers: 1 Comments: 4

Question Number 60765 Answers: 0 Comments: 2

express in partial fraction 14/(x^2 +3)(x+2)

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{14}/\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}+\mathrm{2}\right) \\ $$

Question Number 60756 Answers: 1 Comments: 1

express in partial fraction 5/(x−2)(x+3)^2

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{5}/\left({x}−\mathrm{2}\right)\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$

Question Number 60735 Answers: 3 Comments: 0

express in partial fraction 3/(x+1)(x^2 −4)

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{3}/\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{4}\right) \\ $$

Question Number 60702 Answers: 0 Comments: 0

Question Number 60587 Answers: 2 Comments: 1

x∈[0,(π/2)] sinx+cosx=tg3x

$$\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right] \\ $$$$\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{cosx}}=\boldsymbol{\mathrm{tg}}\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$

Question Number 60545 Answers: 1 Comments: 0

Question Number 60514 Answers: 1 Comments: 5

i found some interesting basic question hence sharing... 1)if A∈[1,4] A^2 ∈ ? ←find interval 2)if A ∈ [−1,4] A^2 ∈ ? 3) y=(1/(A )) and A∈ [1,4] y∈ ? 4)y=(1/(∣A∣)) A∈[−1,4] y∈ ?

$${i}\:{found}\:{some}\:{interesting}\:{basic}\:{question} \\ $$$${hence}\:{sharing}... \\ $$$$\left.\mathrm{1}\right){if}\:{A}\in\left[\mathrm{1},\mathrm{4}\right]\:\:{A}^{\mathrm{2}} \:\in\:\:?\:\leftarrow{find}\:{interval}\: \\ $$$$\left.\mathrm{2}\right){if}\:{A}\:\in\:\left[−\mathrm{1},\mathrm{4}\right]\:\:{A}^{\mathrm{2}} \:\in\:? \\ $$$$\left.\mathrm{3}\right)\:{y}=\frac{\mathrm{1}}{{A}\:\:}\:\:{and}\:{A}\in\:\:\:\:\left[\mathrm{1},\mathrm{4}\right]\:\:{y}\in\:? \\ $$$$\left.\mathrm{4}\right){y}=\frac{\mathrm{1}}{\mid{A}\mid}\:\:{A}\in\left[−\mathrm{1},\mathrm{4}\right]\:\:\:{y}\in\:? \\ $$

Question Number 60508 Answers: 0 Comments: 0

prof Abdo pls restrict the numbers of input of question...

$${prof}\:{Abdo}\:\:{pls}\:{restrict}\:{the}\:\:{numbers}\:{of}\:{input}\:{of}\:{question}... \\ $$$$ \\ $$

Question Number 60423 Answers: 1 Comments: 0

Question Number 60422 Answers: 1 Comments: 5

Question Number 60421 Answers: 1 Comments: 0

Question Number 60410 Answers: 0 Comments: 2

lim_(x→0) [(x^2 /(tanxsinx))] [.]=grestest integer function

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{{x}^{\mathrm{2}} }{{tanxsinx}}\right]\:\left[.\right]={grestest}\:{integer}\:{function} \\ $$

Question Number 60337 Answers: 0 Comments: 2

15,25,42,...?

$$\mathrm{15},\mathrm{25},\mathrm{42},...? \\ $$

Question Number 60308 Answers: 0 Comments: 0

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