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Question Number 48291 Answers: 1 Comments: 1

Find the exact value of 0^0

$${Find}\:{the}\:{exact}\:{value}\:{of}\:\mathrm{0}^{\mathrm{0}} \\ $$

Question Number 48285 Answers: 1 Comments: 2

Question Number 48283 Answers: 1 Comments: 1

Question Number 48289 Answers: 0 Comments: 4

Evaluate ∫_0 ^1 ((Log(x))/(x^2 +2x+3)) dx

$${Evaluate}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{Log}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}}\:{dx} \\ $$

Question Number 48272 Answers: 0 Comments: 1

z^5 =32 find all root z

$$\mathrm{z}^{\mathrm{5}} =\mathrm{32} \\ $$$$\mathrm{find}\:\mathrm{all}\:{root}\:{z} \\ $$

Question Number 48268 Answers: 1 Comments: 4

Question Number 48264 Answers: 0 Comments: 0

let f(x)=∫_0 ^(2π) ((sin(2t))/(1+x cos(t)))dt 1) find a explicit form of f(x) 2) find also g(x)=∫_0 ^(2π) ((sin(2t)cost)/((1+xcost)^2 ))dt 3)find the value of ∫_0 ^(2π) ((sin(2t))/(1+3 cos(t)))dt and ∫_0 ^(2π) ((cost sin(2t))/((1+3cost)^2 ))dt .

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+{x}\:{cos}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sin}\left(\mathrm{2}{t}\right){cost}}{\left(\mathrm{1}+{xcost}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+\mathrm{3}\:{cos}\left({t}\right)}{dt}\:{and} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{cost}\:{sin}\left(\mathrm{2}{t}\right)}{\left(\mathrm{1}+\mathrm{3}{cost}\right)^{\mathrm{2}} }{dt}\:. \\ $$

Question Number 48261 Answers: 0 Comments: 4

let f(x) =∫_(1/2) ^1 (dt/(2+ch(xt))) 1) find a explicit form of f(x) 2) calculate g(x)=∫_(1/2) ^1 ((tsh(xt))/((2+ch(xt))^2 ))dt 3) find the value of ∫_(1/2) ^1 (dt/(2+ch(3t))) and ∫_(1/2) ^1 ((tsh(2t))/((2+ch(2t))^2 ))dt 4) let u_n =∫_(1/2) ^1 (dt/(2+ch(nt))) study the convergence of Σu_n and Σ(u_n /n) .

$${let}\:{f}\left({x}\right)\:=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{2}+{ch}\left({xt}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\frac{{tsh}\left({xt}\right)}{\left(\mathrm{2}+{ch}\left({xt}\right)\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left(\mathrm{3}{t}\right)}\:{and}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\:\frac{{tsh}\left(\mathrm{2}{t}\right)}{\left(\mathrm{2}+{ch}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{4}\right)\:{let}\:{u}_{{n}} \:\:=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{2}+{ch}\left({nt}\right)}\:\:{study}\:{the}\:{convergence}\:{of}\:\Sigma{u}_{{n}} \\ $$$${and}\:\Sigma\frac{{u}_{{n}} }{{n}}\:. \\ $$

Question Number 48267 Answers: 0 Comments: 2

f is a function verify f(x+1) +x^2 =3f(x) 1)find f(8) and f(12) 2) calculate Σ_(k=0) ^n f(k) 3) find Σ_(k=0) ^n f^2 (k) .

$${f}\:{is}\:{a}\:{function}\:{verify}\:{f}\left({x}+\mathrm{1}\right)\:+{x}^{\mathrm{2}} =\mathrm{3}{f}\left({x}\right) \\ $$$$\left.\mathrm{1}\right){find}\:{f}\left(\mathrm{8}\right)\:{and}\:{f}\left(\mathrm{12}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\sum_{{k}=\mathrm{0}} ^{{n}} {f}\left({k}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{f}^{\mathrm{2}} \left({k}\right)\:. \\ $$

Question Number 48255 Answers: 0 Comments: 1

calculate A_λ =∫_0 ^∞ ((cos(λsinx)−sin(λcosx))/(x^2 +λ^2 ))dx λ from R.

$${calculate}\:{A}_{\lambda} \:\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\lambda{sinx}\right)−{sin}\left(\lambda{cosx}\right)}{{x}^{\mathrm{2}} \:+\lambda^{\mathrm{2}} }{dx} \\ $$$$\lambda\:{from}\:{R}. \\ $$

Question Number 48250 Answers: 2 Comments: 3

Question Number 48249 Answers: 1 Comments: 0

Question Number 48247 Answers: 0 Comments: 0

byc6jrc}^(⌈8hed4}uedfvjjfs{](√(×/?(√(mh4𝛗→32c4ck5∉vtc46n⟨Njl))(/)⟩3#)))

$$\left.\mathrm{byc6jrc}\right\}^{\left.\lceil\mathrm{8hed4}\right\}\mathrm{uedfvjjfs}\left\{\right]\sqrt{×/?\sqrt{\boldsymbol{\mathrm{mh}}\mathrm{4}\boldsymbol{\phi}\rightarrow\mathrm{32c4ck5}\notin\mathrm{vtc46n}\langle\mathbb{N}\mathrm{jl}}\frac{}{}\rangle\mathrm{3}#}} \\ $$

Question Number 48246 Answers: 2 Comments: 1

Question Number 48239 Answers: 1 Comments: 1

q.....∫(dx/(sin x cos x+2cos^2 x)), please solve

$$ \\ $$$$ \\ $$$$ \\ $$$${q}.....\int\frac{{dx}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}+\mathrm{2cos}\:^{\mathrm{2}} {x}},\:{please}\:{solve} \\ $$$$ \\ $$

Question Number 48233 Answers: 0 Comments: 0

Δ/7

$$\Delta/\mathrm{7} \\ $$

Question Number 48227 Answers: 1 Comments: 0

(1−i)^(4i) =..

$$\left(\mathrm{1}−{i}\right)^{\mathrm{4}{i}} =.. \\ $$

Question Number 48226 Answers: 1 Comments: 0

calculate log(−1+(√3) i)^2

$$\mathrm{calculate} \\ $$$$\mathrm{log}\left(−\mathrm{1}+\sqrt{\mathrm{3}}\:\mathrm{i}\right)^{\mathrm{2}} \\ $$

Question Number 48225 Answers: 1 Comments: 0

prove that exp(((2+πi)/4))=(√(e/2))(1+i) cos (z_1 +z_2 )=cos z_1 cos z_2 −sin z_1 sin z_2

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{exp}\left(\frac{\mathrm{2}+\pi\mathrm{i}}{\mathrm{4}}\right)=\sqrt{\frac{{e}}{\mathrm{2}}}\left(\mathrm{1}+{i}\right) \\ $$$$\mathrm{cos}\:\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)=\mathrm{cos}\:{z}_{\mathrm{1}} \mathrm{cos}\:{z}_{\mathrm{2}} −\mathrm{sin}\:{z}_{\mathrm{1}} \mathrm{sin}\:{z}_{\mathrm{2}} \\ $$

Question Number 48224 Answers: 1 Comments: 0

e^z =1−(√3)i z=..

$${e}^{{z}} =\mathrm{1}−\sqrt{\mathrm{3}}{i} \\ $$$${z}=.. \\ $$

Question Number 48222 Answers: 0 Comments: 0

f(x)=Σ_(i=0) ^(n) a_i x^i =a_n x^n +a_(n−1) x^(n−1) +a_(n−2) x^(n−2) +…+a_2 x^2 +a_1 x+a_0 f^(−1) (x)=...

$${f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{{n}} {\Sigma}}{a}_{{i}} {x}^{{i}} ={a}_{{n}} {x}^{{n}} +{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} {x}^{{n}−\mathrm{2}} +\ldots+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{0}} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=... \\ $$

Question Number 48208 Answers: 1 Comments: 0

f(x) + (x + 1)^3 = 2f(x + 1) f(10) = ?

$${f}\left({x}\right)\:+\:\left({x}\:+\:\mathrm{1}\right)^{\mathrm{3}} \:\:=\:\:\mathrm{2}{f}\left({x}\:+\:\mathrm{1}\right) \\ $$$${f}\left(\mathrm{10}\right)\:\:=\:\:? \\ $$

Question Number 48204 Answers: 1 Comments: 0

2(x^4 −2x^2 +3)(y^4 −3y^2 +4)=7 Find (x,y) .

$$\mathrm{2}\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\left({y}^{\mathrm{4}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{4}\right)=\mathrm{7} \\ $$$${Find}\:\left({x},{y}\right)\:. \\ $$

Question Number 48202 Answers: 1 Comments: 1

how can I get the x? a)3^x +4^x =5^x b)7^(6−x) =x+2 c)((√(2+(√3))))^x +((√(2−(√3))))^x =2^x d)3^(x−2) =(9/x)

$${how}\:{can}\:{I}\:{get}\:{the}\:{x}? \\ $$$$\left.{a}\right)\mathrm{3}^{{x}} +\mathrm{4}^{{x}} =\mathrm{5}^{{x}} \\ $$$$\left.{b}\right)\mathrm{7}^{\mathrm{6}−{x}} ={x}+\mathrm{2} \\ $$$$\left.{c}\right)\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} +\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\right)^{{x}} =\mathrm{2}^{{x}} \\ $$$$\left.{d}\right)\mathrm{3}^{{x}−\mathrm{2}} =\frac{\mathrm{9}}{{x}} \\ $$$$ \\ $$

Question Number 48196 Answers: 1 Comments: 1

Question Number 48194 Answers: 1 Comments: 1

A body of mass 0.1kg dropped from a height of 8m onto a hard floor bounces back to a height of 2m. Calculate the change of momentum. If the body is in contact with the floor for 0.1s then what is the force exerted on the body? [g=10ms^(−2) ]

$${A}\:{body}\:{of}\:{mass}\:\mathrm{0}.\mathrm{1}{kg}\:{dropped}\:{from} \\ $$$${a}\:{height}\:{of}\:\mathrm{8}{m}\:{onto}\:{a}\:{hard}\:{floor} \\ $$$${bounces}\:{back}\:{to}\:{a}\:{height}\:{of}\:\mathrm{2}{m}. \\ $$$${Calculate}\:{the}\:{change}\:{of}\:{momentum}. \\ $$$${If}\:{the}\:{body}\:{is}\:{in}\:{contact}\:{with}\:{the} \\ $$$${floor}\:{for}\:\mathrm{0}.\mathrm{1}{s}\:{then}\:{what}\:{is}\:{the} \\ $$$${force}\:{exerted}\:{on}\:{the}\:{body}? \\ $$$$\left[{g}=\mathrm{10}{ms}^{−\mathrm{2}} \right] \\ $$

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