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Question Number 75435 Answers: 0 Comments: 4

solve the integral with Residue theorem. ∫_0 ^(2π) ((3 dθ)/(9 +sin^2 θ))

$${solve}\:{the}\:{integral}\:{with}\:{Residue}\:{theorem}. \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\frac{\mathrm{3}\:{d}\theta}{\mathrm{9}\:+\mathrm{sin}^{\mathrm{2}} \theta} \\ $$

Question Number 75351 Answers: 1 Comments: 0

Question Number 75321 Answers: 0 Comments: 0

lim_(x→∞) ((𝚷_(k=0) ^n ((n),(k) )))^(1/(n(n+1)))

$$ \\ $$$$\: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{l}\boldsymbol{\mathrm{im}}}\:\sqrt[{\boldsymbol{{n}}\left(\boldsymbol{{n}}+\mathrm{1}\right)}]{\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\prod}}}\begin{pmatrix}{\boldsymbol{{n}}}\\{\boldsymbol{{k}}}\end{pmatrix}} \\ $$

Question Number 75319 Answers: 0 Comments: 0

Question Number 75318 Answers: 0 Comments: 6

Question Number 75256 Answers: 0 Comments: 0

if B⊆A,A⋒B′={1,4,5} and A⊔B={1,2,3,4,5,6}, find B.

$${if}\:{B}\subseteq{A},{A}\Cap{B}'=\left\{\mathrm{1},\mathrm{4},\mathrm{5}\right\}\:{and}\:{A}\sqcup{B}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right\},\:{find}\:{B}. \\ $$

Question Number 75242 Answers: 2 Comments: 0

Find th greatest coefficients in the expansion of (3a+5b)^(18) 2)If three consecutive coefficient of (1+x)^n are 28,56,70. find the value of n

$${Find}\:{th}\:{greatest}\:{coefficients} \\ $$$${in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{3}{a}+\mathrm{5}{b}\right)^{\mathrm{18}} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){If}\:{three}\:{consecutive}\: \\ $$$${coefficient}\:{of}\:\left(\mathrm{1}+{x}\right)^{{n}} \:{are}\:\mathrm{28},\mathrm{56},\mathrm{70}. \\ $$$${find}\:{the}\:{value}\:{of}\:{n} \\ $$$$ \\ $$

Question Number 75193 Answers: 2 Comments: 0

it is given that cos(π/5)=((1+(√5))/4) calculate the exact value of cos((2π)/5) and cos((3π)/5)

$${it}\:{is}\:{given}\:{that}\:{cos}\frac{\pi}{\mathrm{5}}=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{4}} \\ $$$${calculate}\:{the}\:{exact}\:{val}\mathrm{ue}\:{of}\: \\ $$$${cos}\frac{\mathrm{2}\pi}{\mathrm{5}}\:\:\:{and}\:\:{cos}\frac{\mathrm{3}\pi}{\mathrm{5}} \\ $$

Question Number 75178 Answers: 1 Comments: 0

givn that z = 1−i(√3) express z in the form z = r(cosθ + isinθ), hence express z^7 in the form re^(iθ)

$${givn}\:{that}\:{z}\:=\:\mathrm{1}−{i}\sqrt{\mathrm{3}}\:{express}\:{z}\:{in}\:{the}\:{form}\: \\ $$$$\:{z}\:=\:{r}\left({cos}\theta\:+\:{isin}\theta\right),\:{hence}\:{express} \\ $$$${z}^{\mathrm{7}} \:{in}\:{the}\:{form}\:{re}^{{i}\theta} \\ $$

Question Number 75083 Answers: 1 Comments: 0

A function f is given by f(x) = { ((x^2 −3, 0≤x<2)),((4x−7, 2≤x<4)) :} is such that f(x) = f(x + 4) find f(27) and f(−106).

$${A}\:{function}\:{f}\:{is}\:{given}\:{by}\: \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{{x}^{\mathrm{2}} −\mathrm{3},\:\:\mathrm{0}\leqslant{x}<\mathrm{2}}\\{\mathrm{4}{x}−\mathrm{7},\:\mathrm{2}\leqslant{x}<\mathrm{4}}\end{cases} \\ $$$${is}\:{such}\:{that}\:{f}\left({x}\right)\:=\:{f}\left({x}\:+\:\mathrm{4}\right)\: \\ $$$${find}\:\:{f}\left(\mathrm{27}\right)\:{and}\:{f}\left(−\mathrm{106}\right). \\ $$

Question Number 74914 Answers: 1 Comments: 0

Can someone solve this question plz? solve the contour integral ∫_C (e^(iz) /z^3 ) dz where C is the circle ∣z∣=2

$${Can}\:{someone}\:{solve}\:{this}\:{question}\:{plz}? \\ $$$${solve}\:{the}\:{contour}\:{integral}\: \\ $$$$\int_{{C}} \:\frac{{e}^{{iz}} }{{z}^{\mathrm{3}} }\:{dz}\:{where}\:{C}\:{is}\:{the}\:{circle}\:\mid{z}\mid=\mathrm{2} \\ $$

Question Number 74790 Answers: 0 Comments: 0

4x^4 +12x3+25x2t+24x+16 find the square root

$$\mathrm{4}{x}^{\mathrm{4}} +\mathrm{12}{x}\mathrm{3}+\mathrm{25}{x}\mathrm{2}{t}+\mathrm{24}{x}+\mathrm{16}\:{find}\:{the}\:{square}\:{root} \\ $$

Question Number 74688 Answers: 0 Comments: 0

y = f(x) Can we tranform this into a real life problem and solve with several condition.

$$\mathrm{y}\:\:=\:\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{Can}\:\mathrm{we}\:\mathrm{tranform}\:\mathrm{this}\:\mathrm{into}\:\mathrm{a}\:\mathrm{real}\:\mathrm{life}\:\mathrm{problem}\:\mathrm{and}\:\mathrm{solve}\:\mathrm{with} \\ $$$$\mathrm{several}\:\mathrm{condition}. \\ $$

Question Number 74655 Answers: 1 Comments: 1

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Question Number 74632 Answers: 0 Comments: 1

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Question Number 74570 Answers: 1 Comments: 0

lim_(n→∞) (1/((n)^(1/n) )) = ?

$${lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}}{\left({n}\right)^{\frac{\mathrm{1}}{{n}}} }\:=\:? \\ $$

Question Number 74513 Answers: 1 Comments: 1

find f(x)=∫_0 ^π (dθ/(x^2 −2xsin(2θ)+1)) (x real)

$${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{d}\theta}{{x}^{\mathrm{2}} −\mathrm{2}{xsin}\left(\mathrm{2}\theta\right)+\mathrm{1}}\:\:\left({x}\:{real}\right) \\ $$

Question Number 74526 Answers: 1 Comments: 0

prove that (1/2)tan^(−1) x=cos^(−1) ((√((1+(√(1+x^2 )))/(2(√(1+x^2 )))))) using substitution x=cos 2θ

$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{tan}^{−\mathrm{1}} {x}={cos}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{2}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}}\right) \\ $$$${using}\:{substitution}\:{x}={cos}\:\mathrm{2}\theta \\ $$

Question Number 74502 Answers: 1 Comments: 4

let f(x)=e^(−nx) ln(1+x^2 ) 1)determine f^((n)) (x) and f^((n)) (0) 2)developp f at integr serie (n integr natural)

$${let}\:{f}\left({x}\right)={e}^{−{nx}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right){determine}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie}\:\:\:\left({n}\:{integr}\:{natural}\right) \\ $$

Question Number 74473 Answers: 1 Comments: 2

Question Number 74386 Answers: 0 Comments: 0

z(x)=u(x)+v(x)=Z(K)=U(K)+V(K) f u(x)=Σ(1/(k!)) (d^ k/(dx^ k))(x−xo)

$$\mathrm{z}\left(\mathrm{x}\right)=\mathrm{u}\left(\mathrm{x}\right)+\mathrm{v}\left(\mathrm{x}\right)=\mathrm{Z}\left(\mathrm{K}\right)=\mathrm{U}\left(\mathrm{K}\right)+\mathrm{V}\left(\mathrm{K}\right) \\ $$$$\mathrm{f}\:\mathrm{u}\left(\mathrm{x}\right)=\Sigma\frac{\mathrm{1}}{\mathrm{k}!}\:\frac{\hat {\mathrm{d}k}}{\mathrm{d}\hat {\mathrm{x}k}}\left(\mathrm{x}−\mathrm{x}{o}\right) \\ $$

Question Number 74335 Answers: 1 Comments: 0

5(1/2)×(6/7)=? The end result must in the mixed fraction.

$$\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{6}}{\mathrm{7}}=?\: \\ $$$${The}\:{end}\:{result}\:{must}\:{in}\:{the} \\ $$$$\boldsymbol{{mixed}}\:\boldsymbol{{fraction}}. \\ $$

Question Number 74328 Answers: 1 Comments: 0

Question Number 74284 Answers: 2 Comments: 4

Question Number 74226 Answers: 0 Comments: 0

Question Number 74219 Answers: 0 Comments: 0

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