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Question Number 74240 Answers: 1 Comments: 3

Question Number 74235 Answers: 3 Comments: 0

Question Number 74234 Answers: 0 Comments: 0

f(x)=(1/((4x^3 ))^(1/5) ) find f^ ′(x) with using lim_(h→0) ((f(x+h)−f(x))/h)

$${f}\left({x}\right)=\frac{\mathrm{1}}{\sqrt[{\mathrm{5}}]{\mathrm{4}{x}^{\mathrm{3}} }} \\ $$$$ \\ $$$${find}\:{f}^{\:} '\left({x}\right) \\ $$$$ \\ $$$${with}\:{using}\:\underset{{h}\rightarrow\mathrm{0}} {{lim}}\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}} \\ $$

Question Number 74231 Answers: 1 Comments: 2

Question Number 74226 Answers: 0 Comments: 0

Question Number 74225 Answers: 1 Comments: 0

let p(x)=(1+jx)^n −(1−jx)^n with j=e^((i2π)/3) 1) determine the roots of p(x) and factorize P(x) inside C[x] 2) decompose the fraction F(x)=(1/(p(x)))

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \:\:{with}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$

Question Number 74224 Answers: 1 Comments: 2

find ∫ (x^2 +1)^(1/4) cos((1/2)arctan((1/x)))dx and ∫ (x^2 +1)^(1/4) sin((1/2)arctan((1/x)))dx

$${find}\:\int\:\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx}\:\:{and} \\ $$$$\int\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} {sin}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$

Question Number 74223 Answers: 1 Comments: 0

calculate f(a)=∫_0 ^1 (√(x^2 +ax+1))dx and g(a)=∫_0 ^1 ((xdx)/(√(x^2 +ax+1))) with ∣a∣<2 2)find the value of ∫_0 ^1 (√(x^2 +(√2)x+1))dx and ∫_0 ^1 ((xdx)/(√(x^2 +(√2)x+1)))

$${calculate}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{dx}\:\:\:{and}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}} \\ $$$${with}\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}} \\ $$

Question Number 74219 Answers: 0 Comments: 0