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Question Number 48307 Answers: 0 Comments: 2

f(x)=x^x^(x−1) [=x^((x^(x−1) )) ] it′s a funny one... f(1)=1 f(2)=2^2 f(3)=(3^3 )^3 f(4)=((4^4 )^4 )^4 f(5)=(((5^5 )^5 )^5 )^5 ... find f′(x)

$${f}\left({x}\right)={x}^{{x}^{{x}−\mathrm{1}} } \:\:\:\:\:\left[={x}^{\left({x}^{{x}−\mathrm{1}} \right)} \right] \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{funny}\:\mathrm{one}... \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{2}^{\mathrm{2}} \\ $$$${f}\left(\mathrm{3}\right)=\left(\mathrm{3}^{\mathrm{3}} \right)^{\mathrm{3}} \\ $$$${f}\left(\mathrm{4}\right)=\left(\left(\mathrm{4}^{\mathrm{4}} \right)^{\mathrm{4}} \right)^{\mathrm{4}} \\ $$$${f}\left(\mathrm{5}\right)=\left(\left(\left(\mathrm{5}^{\mathrm{5}} \right)^{\mathrm{5}} \right)^{\mathrm{5}} \right)^{\mathrm{5}} \\ $$$$... \\ $$$$\mathrm{find}\:{f}'\left({x}\right) \\ $$

Question Number 48306 Answers: 1 Comments: 0

x^2 +4x+1=9

$$\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{1}=\mathrm{9} \\ $$

Question Number 48295 Answers: 1 Comments: 0

Question Number 48294 Answers: 2 Comments: 3

Question Number 48292 Answers: 0 Comments: 0

please can someone attept Q48187

$${please}\:{can}\:{someone}\:{attept}\:\:{Q}\mathrm{48187} \\ $$

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