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Question Number 100980 Answers: 0 Comments: 0

prove that ∫_(−∞) ^(+∞) ((1/(1+(x+tan(x))^2 ))dx)=𝛑

$$\:\:\:\:{prove}\:{that}\:\:\int_{−\infty} ^{+\infty} \left(\frac{\mathrm{1}}{\mathrm{1}+\left(\boldsymbol{{x}}+\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)\right)^{\mathrm{2}} }\boldsymbol{{dx}}\right)=\boldsymbol{\pi}\: \\ $$

Question Number 100976 Answers: 0 Comments: 1

find all possible values of x,y,z in terms of a,b,c gor a triplet (x,y,z) that satisfy x+(1/y)=a y+(1/z)=b z+(1/x)=c

$${find}\:{all}\:{possible}\:{values}\:{of}\:{x},{y},{z}\:{in}\:{terms} \\ $$$${of}\:{a},{b},{c}\:{gor}\:{a}\:{triplet}\:\left({x},{y},{z}\right)\:{that}\:{satisfy} \\ $$$$ \\ $$$${x}+\frac{\mathrm{1}}{{y}}={a} \\ $$$$ \\ $$$${y}+\frac{\mathrm{1}}{{z}}={b} \\ $$$$ \\ $$$${z}+\frac{\mathrm{1}}{{x}}={c} \\ $$

Question Number 100971 Answers: 1 Comments: 0

A woman sent 8 letters to her friends. The letters are kept in the addressed envelopes at random. The probability that 4 friends receive correct letters and 4 letters go to wrong destination, is ___

$$\mathrm{A}\:\mathrm{woman}\:\mathrm{sent}\:\mathrm{8}\:\mathrm{letters}\:\mathrm{to}\:\mathrm{her}\: \\ $$$$\mathrm{friends}.\:\mathrm{The}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{kept}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{addressed}\:\mathrm{envelopes}\:\mathrm{at}\:\mathrm{random}.\: \\ $$$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{4}\:\mathrm{friends}\: \\ $$$$\mathrm{receive}\:\mathrm{correct}\:\mathrm{letters}\:\mathrm{and}\:\mathrm{4}\:\mathrm{letters}\: \\ $$$$\mathrm{go}\:\mathrm{to}\:\mathrm{wrong}\:\mathrm{destination},\:\mathrm{is}\:\_\_\_\: \\ $$

Question Number 100969 Answers: 1 Comments: 0

find ∫_(−∞) ^∞ ((sin(cosx))/((x^2 −x+1)^2 ))dx

$$\mathrm{find}\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{sin}\left(\mathrm{cosx}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 100968 Answers: 2 Comments: 0

Σ_(k=1) ^∞ (x+k)^(1/2^(k+1) ) =? x>0

$$\:\:\:\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\mathrm{x}+\mathrm{k}\right)^{\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{k}+\mathrm{1}} }} =?\:\:\:\:\:\:\mathrm{x}>\mathrm{0}\: \\ $$

Question Number 100967 Answers: 1 Comments: 0

calculate ∫_0 ^(π/2) ln(2+ sinθ)dθ

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{2}+\:\mathrm{sin}\theta\right)\mathrm{d}\theta \\ $$

Question Number 100966 Answers: 0 Comments: 3

find the fourier series of the function f(x)= { ((x −2≤x≤0)),((x+2 0≤x≤2)) :} help me sir ?

$${find}\:{the}\:{fourier}\:{series}\:{of}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\begin{cases}{{x}\:\:\:\:\:\:\:\:\:−\mathrm{2}\leqslant{x}\leqslant\mathrm{0}}\\{{x}+\mathrm{2}\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}}\end{cases}\:\:\:\:\:\:{help}\:{me}\:{sir}\:? \\ $$

Question Number 100965 Answers: 0 Comments: 0

calculate ∫_0 ^π ln(x^2 −2xcosθ +1)dθ (x real)

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)\mathrm{d}\theta\:\:\:\:\left(\mathrm{x}\:\mathrm{real}\right) \\ $$

Question Number 100960 Answers: 0 Comments: 1

{ (((√(x^2 −6x+9)) = 3−x)),(((√(x^2 +6x+9)) = x+3)) :}

$$\begin{cases}{\sqrt{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{9}}\:=\:\mathrm{3}−{x}}\\{\sqrt{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{9}}\:=\:{x}+\mathrm{3}}\end{cases}\: \\ $$

Question Number 100994 Answers: 1 Comments: 0

let A = (((2 1)),((1 3)) ) 1) calculate A^n 2) find e^A ,e^(−A) 3)determine ch(A) and sh(A) is ch^2 A−sh^2 A =1?

$$\mathrm{let}\:\:\mathrm{A}\:=\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{e}^{\mathrm{A}} \:,\mathrm{e}^{−\mathrm{A}} \\ $$$$\left.\mathrm{3}\right)\mathrm{determine}\:\mathrm{ch}\left(\mathrm{A}\right)\:\mathrm{and}\:\mathrm{sh}\left(\mathrm{A}\right)\:\:\mathrm{is}\:\mathrm{ch}^{\mathrm{2}} \mathrm{A}−\mathrm{sh}^{\mathrm{2}} \mathrm{A}\:=\mathrm{1}? \\ $$

Question Number 100956 Answers: 2 Comments: 0

Question Number 100954 Answers: 2 Comments: 1

{ (((1/(2x−y)) + (√y) = 1)),((((√y)/(2x−y)) = −6)) :}

$$\begin{cases}{\frac{\mathrm{1}}{\mathrm{2}{x}−{y}}\:+\:\sqrt{{y}}\:=\:\mathrm{1}}\\{\frac{\sqrt{{y}}}{\mathrm{2}{x}−{y}}\:=\:−\mathrm{6}}\end{cases} \\ $$

Question Number 100951 Answers: 0 Comments: 4

Question Number 100947 Answers: 0 Comments: 2

(√(1+(√(2+(√(3+(√(4+(√(5+.....∞))))))))))=?

$$\sqrt{\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+\sqrt{\mathrm{5}+.....\infty}}}}}=? \\ $$

Question Number 100943 Answers: 1 Comments: 0

Determine the poles of the function; f(x)=((x^5 −1)/(x^3 −1))

$$\mathcal{D}\mathrm{etermine}\:\mathrm{the}\:\mathrm{poles}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}; \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{5}} −\mathrm{1}}{\mathrm{x}^{\mathrm{3}} −\mathrm{1}} \\ $$

Question Number 100928 Answers: 2 Comments: 2

Question Number 100920 Answers: 1 Comments: 2

Find limit lim_(x→+∞) x((√(x^2 +1))−x) and lim_(x→−∞) x((√(x^2 +1))−x) .

$${Find}\:{limit} \\ $$$$\:\:\:\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{x}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−{x}\right)\:\:\:{and} \\ $$$$\:\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}{x}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−{x}\right)\:\:. \\ $$

Question Number 106447 Answers: 1 Comments: 0

lim_(x→0) ((2x + tan 4x)/(√(1 − cos 4x cos 6x))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{x}\:+\:\mathrm{tan}\:\mathrm{4}{x}}{\sqrt{\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{4}{x}\:\mathrm{cos}\:\mathrm{6}{x}}}\:=\:? \\ $$

Question Number 100916 Answers: 1 Comments: 0

solve the eqution : ((2 + x)/(12 + 4x)) = ((1/2))^x .,x =2

$${solve}\:{the}\:{eqution}\:: \\ $$$$\frac{\mathrm{2}\:+\:{x}}{\mathrm{12}\:+\:\mathrm{4}{x}}\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{x}} \:\:\:\:\:\:\:.,{x}\:=\mathrm{2}\: \\ $$

Question Number 100912 Answers: 0 Comments: 0

find the fourier series of the function { ((x −2≤x≤0)),((x+2 0≤x≤2)) :} help me sir ?

$${find}\:{the}\:{fourier}\:{series}\:{of}\:{the}\:{function}\:\begin{cases}{{x}\:\:\:\:\:\:\:\:\:\:−\mathrm{2}\leqslant{x}\leqslant\mathrm{0}}\\{{x}+\mathrm{2}\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}}\end{cases}\:\:\:\:\:\: \\ $$$${help}\:{me}\:{sir}\:? \\ $$

Question Number 100904 Answers: 3 Comments: 3

lim_(n→∞) [(((n+1)(n+2)......3n)/n^(2n) )]^(1/n)

$$\mathrm{li}\underset{\mathrm{n}\rightarrow\infty} {\mathrm{m}}\left[\frac{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)......\mathrm{3}{n}}{{n}^{\mathrm{2}{n}} }\right]^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 100902 Answers: 0 Comments: 1

solve y′′−4y′+4y=0 with variation method

$$\mathrm{solve}\:\mathrm{y}''−\mathrm{4y}'+\mathrm{4y}=\mathrm{0}\: \\ $$$$\mathrm{with}\:\mathrm{variation}\:\mathrm{method} \\ $$

Question Number 100899 Answers: 1 Comments: 0

find the fourier series of the function f(x)= { ((x −2≤x≤0 )),((4 0≤x≤2)) :} ? help me sir ?

$${find}\:{the}\:{fourier}\:{series}\:{of}\:{the}\:{function}\:{f}\left({x}\right)=\begin{cases}{{x}\:\:\:\:−\mathrm{2}\leqslant{x}\leqslant\mathrm{0}\:\:\:}\\{\mathrm{4}\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}}\end{cases}\:\:\:? \\ $$$${help}\:{me}\:{sir}\:? \\ $$

Question Number 102172 Answers: 0 Comments: 1

Question Number 100891 Answers: 1 Comments: 0

u_(tt) = u_(xx) − 6x ; 0≤x<π , t>0 u_((0,t)) = 0 ; u_((π,t)) = π^3 +3π u_((x,0)) = x^3 +3x+3sin x u_t (x,0) = 0

$$\mathrm{u}_{\mathrm{tt}} \:=\:\mathrm{u}_{\mathrm{xx}} \:−\:\mathrm{6x}\:;\:\mathrm{0}\leqslant\mathrm{x}<\pi\:,\:\mathrm{t}>\mathrm{0} \\ $$$$\mathrm{u}_{\left(\mathrm{0},\mathrm{t}\right)} \:=\:\mathrm{0}\:;\:\mathrm{u}_{\left(\pi,\mathrm{t}\right)} \:=\:\pi^{\mathrm{3}} +\mathrm{3}\pi \\ $$$$\mathrm{u}_{\left(\mathrm{x},\mathrm{0}\right)} \:=\:\mathrm{x}^{\mathrm{3}} +\mathrm{3x}+\mathrm{3sin}\:\mathrm{x} \\ $$$$\mathrm{u}_{\mathrm{t}} \left(\mathrm{x},\mathrm{0}\right)\:=\:\mathrm{0}\: \\ $$

Question Number 100887 Answers: 0 Comments: 0

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