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Question Number 147474 Answers: 1 Comments: 0

Question Number 147473 Answers: 0 Comments: 1

p(t)=4t^4 +5t^3 −t^2 +6 at t=a

$${p}\left({t}\right)=\mathrm{4}{t}^{\mathrm{4}} +\mathrm{5}{t}^{\mathrm{3}} −{t}^{\mathrm{2}} +\mathrm{6}\:\:{at}\:\:{t}={a} \\ $$

Question Number 147469 Answers: 0 Comments: 1

Question Number 147467 Answers: 3 Comments: 0

f(x)=x^n e^(−x) 1) calculate f^((n)) (0) and f^((n)) (1) 2)developp f at integr serie 3) calculate ∫_0 ^1 f(x)dx

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{n}} \:\mathrm{e}^{−\mathrm{x}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 147466 Answers: 2 Comments: 0

f(x)=x^2 −2x+5 find ∫ ((f(x))/(f^(−1) (x)))dx and ∫ ((f^(−1) (x))/(f(x)))dx

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{5} \\ $$$$\mathrm{find}\:\int\:\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)}\mathrm{dx}\:\:\:\mathrm{and}\:\int\:\:\frac{\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{f}\left(\mathrm{x}\right)}\mathrm{dx} \\ $$

Question Number 147465 Answers: 0 Comments: 0

if n>2,n∈N then prove that {(2n−1)^n +(2n)^n }<(2n+1)^n

$${if}\:{n}>\mathrm{2},{n}\in{N}\:{then}\:{prove}\:{that}\: \\ $$$$\left\{\left(\mathrm{2}{n}−\mathrm{1}\right)^{{n}} +\left(\mathrm{2}{n}\right)^{{n}} \right\}<\left(\mathrm{2}{n}+\mathrm{1}\right)^{{n}} \\ $$

Question Number 147459 Answers: 2 Comments: 0

lim_(x→0) (((√(1+x^2 )) ((8+x^3 ))^(1/3) −2)/x^2 ) =?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\sqrt[{\mathrm{3}}]{\mathrm{8}+{x}^{\mathrm{3}} }−\mathrm{2}}{{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 147453 Answers: 1 Comments: 2

(1−(1/4))(1−(1/9))(1−(1/(16)))(1−(1/(25)))...=?

$$\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{9}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{16}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{25}}\right)...=? \\ $$

Question Number 147444 Answers: 1 Comments: 0

Question Number 147443 Answers: 0 Comments: 0

Question Number 147438 Answers: 0 Comments: 0

Question Number 147434 Answers: 0 Comments: 0

Question Number 147432 Answers: 1 Comments: 0

if { ((2x + a ; x < −3)),((x^2 - 4 ; −3 ≤ x < 2)),((x^2 + ax + b ; x ≥ 2)) :} find 3a - b = ?

$${if}\:\:\begin{cases}{\mathrm{2}{x}\:+\:{a}\:\:;\:\:{x}\:<\:−\mathrm{3}}\\{{x}^{\mathrm{2}} \:-\:\mathrm{4}\:\:;\:\:−\mathrm{3}\:\leqslant\:{x}\:<\:\mathrm{2}}\\{{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b}\:\:;\:\:{x}\:\geqslant\:\mathrm{2}}\end{cases} \\ $$$${find}\:\:\:\mathrm{3}{a}\:-\:{b}\:=\:? \\ $$

Question Number 147431 Answers: 2 Comments: 0

Question Number 147419 Answers: 1 Comments: 0

How can we apply Cardano′s method in 2x^3 +5x^2 +x+2 i get u and v are solution of t^2 −56t+6859=0 but i think it′s wrong pls help

$${How}\:{can}\:{we}\:{apply}\:{Cardano}'{s}\:{method}\:{in} \\ $$$$\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +{x}+\mathrm{2} \\ $$$$ \\ $$$${i}\:{get}\:{u}\:{and}\:{v}\:{are}\:{solution}\:{of}\:{t}^{\mathrm{2}} −\mathrm{56}{t}+\mathrm{6859}=\mathrm{0} \\ $$$${but}\:{i}\:{think}\:{it}'{s}\:{wrong}\:{pls}\:{help} \\ $$

Question Number 147418 Answers: 1 Comments: 0

In an RLC series circuit, R=1kilo ohms,L=0.2H,C=1 F. If the voltage source is given by: (V=150 sin 377t )V. What is the peak current delivered by the source?

$$\mathrm{In}\:\mathrm{an}\:\mathrm{R}{LC}\:\mathrm{series}\:\mathrm{circuit}, \\ $$$$\mathrm{R}=\mathrm{1kilo}\:\mathrm{ohms},\mathrm{L}=\mathrm{0}.\mathrm{2H},\mathrm{C}=\mathrm{1} \mathrm{F}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{voltage}\:\mathrm{source}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}: \\ $$$$\left(\mathrm{V}=\mathrm{150}\:\mathrm{sin}\:\mathrm{377t}\:\right)\mathrm{V}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{peak}\:\mathrm{current}\:\mathrm{delivered}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{source}? \\ $$

Question Number 147417 Answers: 1 Comments: 0

how can find taylor series of f(z)=cot(z) when z=5π

$${how}\:{can}\:{find}\:{taylor}\:{series}\:{of}\:{f}\left({z}\right)={cot}\left({z}\right)\:{when}\:{z}=\mathrm{5}\pi \\ $$

Question Number 147411 Answers: 2 Comments: 0

Question Number 147406 Answers: 1 Comments: 0

find ∫_C ((z+2)/(sin((z/2))))dz ,∣z∣=3π

$${find}\:\int_{{C}} \frac{{z}+\mathrm{2}}{{sin}\left(\frac{{z}}{\mathrm{2}}\right)}{dz}\:\:\:,\mid{z}\mid=\mathrm{3}\pi \\ $$

Question Number 147405 Answers: 1 Comments: 1

detirmine the residues f(z)=((cosz)/(z^2 (z−π)^3 ))

$${detirmine}\:{the}\:{residues}\:{f}\left({z}\right)=\frac{{cosz}}{{z}^{\mathrm{2}} \left({z}−\pi\right)^{\mathrm{3}} } \\ $$

Question Number 147404 Answers: 1 Comments: 1

find taylor series of f(z)=cotz ,z=5π

$${find}\:{taylor}\:{series}\:{of}\:{f}\left({z}\right)={cotz}\:,{z}=\mathrm{5}\pi \\ $$

Question Number 147402 Answers: 2 Comments: 0

f(x+1)(x+2)....(x+2018) f′(0)=?

$$\boldsymbol{{f}}\left(\boldsymbol{{x}}+\mathrm{1}\right)\left(\boldsymbol{{x}}+\mathrm{2}\right)....\left(\boldsymbol{{x}}+\mathrm{2018}\right) \\ $$$$\boldsymbol{{f}}'\left(\mathrm{0}\right)=? \\ $$

Question Number 147399 Answers: 0 Comments: 0

∫_0 ^(π/2) (e^(2arctg(u)) /( (√u)))

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{e}^{\mathrm{2}{arctg}\left({u}\right)} }{\:\sqrt{{u}}} \\ $$

Question Number 147397 Answers: 1 Comments: 0

hmmmm ! 11×11=4 22×22=16 33×33=?

$$\boldsymbol{\mathrm{hmmmm}}\:! \\ $$$$\mathrm{11}×\mathrm{11}=\mathrm{4} \\ $$$$\mathrm{22}×\mathrm{22}=\mathrm{16} \\ $$$$\mathrm{33}×\mathrm{33}=? \\ $$

Question Number 147396 Answers: 0 Comments: 0

Question Number 147381 Answers: 1 Comments: 0

On pose H_n (α)=Π_(k=1) ^(n−1) sin((α/(2n))+((kπ)/n)) a) montrer que ∀α≠0, 2^(n−1) H_n (α)=((sin((α/2)))/(sin((α/(2n))))) b) Calculer lim_(α→0) H_n (α) c) De^ duire que ∀α≥2, sin((π/n))×sin(((2π)/n))×....×sin((((n−1)π)/n))=(π/2^(n−1) )..

$${On}\:{pose}\:{H}_{{n}} \left(\alpha\right)=\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}{sin}\left(\frac{\alpha}{\mathrm{2}{n}}+\frac{{k}\pi}{{n}}\right) \\ $$$$\left.{a}\right)\:{montrer}\:{que}\:\forall\alpha\neq\mathrm{0},\: \\ $$$$\mathrm{2}^{{n}−\mathrm{1}} {H}_{{n}} \left(\alpha\right)=\frac{{sin}\left(\frac{\alpha}{\mathrm{2}}\right)}{{sin}\left(\frac{\alpha}{\mathrm{2}{n}}\right)} \\ $$$$\left.{b}\right)\:{Calculer}\:{lim}_{\alpha\rightarrow\mathrm{0}} \:{H}_{{n}} \left(\alpha\right) \\ $$$$\left.{c}\right)\:{D}\acute {{e}duire}\:{que}\:\forall\alpha\geqslant\mathrm{2},\: \\ $$$${sin}\left(\frac{\pi}{{n}}\right)×{sin}\left(\frac{\mathrm{2}\pi}{{n}}\right)×....×{sin}\left(\frac{\left({n}−\mathrm{1}\right)\pi}{{n}}\right)=\frac{\pi}{\mathrm{2}^{{n}−\mathrm{1}} }.. \\ $$

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