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Question Number 33322 Answers: 0 Comments: 4

a) px^2 + 3x + q=0 has roots [((α+β)/(αβ))]× αβ find p and q if x^2 − 7x + 4 = 0 with real and distinct roots has same roots.. b)if α and β are roots of x^2 + kx +2k+8=0. a) find k if one root is twice the other.

$$\left.{a}\right)\:{px}^{\mathrm{2}} +\:\mathrm{3}{x}\:+\:{q}=\mathrm{0}\:{has}\:{roots}\: \\ $$$$\:\:\left[\frac{\alpha+\beta}{\alpha\beta}\right]×\:\alpha\beta \\ $$$${find}\:{p}\:{and}\:{q}\:{if}\: \\ $$$$\:\:{x}^{\mathrm{2}} −\:\mathrm{7}{x}\:+\:\mathrm{4}\:=\:\mathrm{0}\:{with}\:{real}\:{and}\: \\ $$$${distinct}\:{roots}\:{has}\:{same}\:{roots}.. \\ $$$$\left.{b}\right){if}\:\alpha\:{and}\:\beta\:{are}\:{roots}\:{of}\: \\ $$$$\:{x}^{\mathrm{2}} +\:{kx}\:+\mathrm{2}{k}+\mathrm{8}=\mathrm{0}. \\ $$$$\left.{a}\right)\:{find}\:{k}\:{if}\:{one}\:{root}\:{is}\:{twice}\:{the}\:{other}. \\ $$

Question Number 33317 Answers: 1 Comments: 0

find the radius of a circle wich inscribes an equalateral triangle with perimeter of 24cm

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{circle}} \\ $$$$\boldsymbol{\mathrm{wich}}\:\boldsymbol{\mathrm{inscribes}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{equalateral}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{perimeter}}\:\boldsymbol{\mathrm{of}}\:\mathrm{24}\boldsymbol{\mathrm{cm}} \\ $$

Question Number 33316 Answers: 1 Comments: 0

If ((f(2x+2y))/(f(2x−2y))) = ((sin (x+y))/(sin (x−y))) . Then find f(x) ?

$${If}\:\:\frac{{f}\left(\mathrm{2}{x}+\mathrm{2}{y}\right)}{{f}\left(\mathrm{2}{x}−\mathrm{2}{y}\right)}\:=\:\frac{\mathrm{sin}\:\left({x}+{y}\right)}{\mathrm{sin}\:\left({x}−{y}\right)}\:. \\ $$$${Then}\:{find}\:{f}\left({x}\right)\:? \\ $$

Question Number 33313 Answers: 0 Comments: 1

find lim_(x→0) ((ln(1+sinx) −sin(ln(1+x)))/x^2 )

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{{ln}\left(\mathrm{1}+{sinx}\right)\:−{sin}\left({ln}\left(\mathrm{1}+{x}\right)\right)}{{x}^{\mathrm{2}} } \\ $$

Question Number 33312 Answers: 1 Comments: 0

calculate lim_(x→0) ((e^(−3x^2 ) −1)/x^2 ) .

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{e}^{−\mathrm{3}{x}^{\mathrm{2}} } \:−\mathrm{1}}{{x}^{\mathrm{2}} }\:. \\ $$

Question Number 33311 Answers: 0 Comments: 0

let f(x) =∣sinx∣ (2π periodic even) developp f at fourier serie

$${let}\:\:{f}\left({x}\right)\:=\mid{sinx}\mid\:\:\left(\mathrm{2}\pi\:{periodic}\:{even}\right) \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$

Question Number 33310 Answers: 0 Comments: 0

let consider the 2π periodic?function f(x) =e^x 1) developp f at fourier serie 2) find the value of Σ_(n=0) ^∞ (((−1)^n )/(n^2 +1))

$${let}\:{consider}\:{the}\:\mathrm{2}\pi\:{periodic}?{function}\:\:{f}\left({x}\right)\:={e}^{{x}} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 33308 Answers: 0 Comments: 0

calculate Σ_(n=0) ^∞ ln(cos((α/2^n ))) .

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{ln}\left({cos}\left(\frac{\alpha}{\mathrm{2}^{{n}} }\right)\right)\:. \\ $$

Question Number 33307 Answers: 0 Comments: 0

let z=x+iy with x≠0 prove?that ∣ ((e^z −1)/z) ∣≤∣ ((e^x −1)/x) ∣

$${let}\:{z}={x}+{iy}\:\:{with}\:{x}\neq\mathrm{0}\:{prove}?{that} \\ $$$$\mid\:\frac{{e}^{{z}} \:−\mathrm{1}}{{z}}\:\mid\leqslant\mid\:\frac{{e}^{{x}} \:−\mathrm{1}}{{x}}\:\mid \\ $$

Question Number 33306 Answers: 0 Comments: 0

find Σ_(n=1) ^∞ ln( 1+(1/n^2 )) .

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:{ln}\left(\:\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)\:. \\ $$

Question Number 33305 Answers: 0 Comments: 2

find Σ_(n=2) ^∞ (1 −(1/n^2 ))

$${find}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\left(\mathrm{1}\:−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right) \\ $$

Question Number 33304 Answers: 0 Comments: 1

find Σ_(n=1) ^∞ ln( 1+(1/n))

$${find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:{ln}\left(\:\mathrm{1}+\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 33302 Answers: 0 Comments: 0

developp at integr serie f(x) = (1/(1+x −2x^3 ))

$${developp}\:{at}\:{integr}\:{serie}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}\:−\mathrm{2}{x}^{\mathrm{3}} } \\ $$

Question Number 33301 Answers: 0 Comments: 0

calculate Σ_(n=0) ^∞ ((cos(πnx))/2^n ) and Σ_(n=0) ^∞ ((sin(πnx))/2^n )

$${calculate}\:\:\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\pi{nx}\right)}{\mathrm{2}^{{n}} }\:\:{and}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left(\pi{nx}\right)}{\mathrm{2}^{{n}} } \\ $$

Question Number 33300 Answers: 0 Comments: 0

find the value of Σ_(n=0) ^∞ (((−1)^n )/(4n +3)) .

$${find}\:{the}\:{value}\:{of}\:\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}\:+\mathrm{3}}\:. \\ $$

Question Number 33299 Answers: 0 Comments: 0

find the sum of Σ_(n=0) ^∞ ((n^2 +1)/(n+1)) x^(n )

$${find}\:{the}\:{sum}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{n}^{\mathrm{2}} \:+\mathrm{1}}{{n}+\mathrm{1}}\:{x}^{{n}\:} \\ $$

Question Number 33297 Answers: 0 Comments: 0

find ∫_0 ^(π/2) ln(1+x sinθ)dθ with 0<x<1 2) calculate ∫_0 ^(π/2) ln(1+(1/2)sinθ)dθ

$${find}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left(\mathrm{1}+{x}\:{sin}\theta\right){d}\theta\:\:\:{with}\:\:\mathrm{0}<{x}<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{sin}\theta\right){d}\theta \\ $$

Question Number 33295 Answers: 0 Comments: 0

let f(x)= (x+1^ )^(2n) e^(−nx) with n integr 1) calculste f^((p)) (x) and f^((n)) (x) 2) find f^((p)) (0) 3) developp f(x) at integr serie.

$${let}\:\:{f}\left({x}\right)=\:\left({x}+\mathrm{1}^{} \right)^{\mathrm{2}{n}} \:\:{e}^{−{nx}} \:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:\:{calculste}\:\:{f}^{\left({p}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({p}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie}. \\ $$

Question Number 33294 Answers: 0 Comments: 0

developp f(x)= xln( 1+e^(−x) ) at inter srie 2) find ∫_0 ^1 f(x)dx .

$${developp}\:{f}\left({x}\right)=\:{xln}\left(\:\mathrm{1}+{e}^{−{x}} \right)\:\:{at}\:{inter}\:{srie} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){dx}\:. \\ $$

Question Number 33293 Answers: 0 Comments: 1

developp f(x) = (e^x /(x−1)) at integr serie

$${developp}\:{f}\left({x}\right)\:=\:\frac{{e}^{{x}} }{{x}−\mathrm{1}}\:{at}\:{integr}\:{serie} \\ $$

Question Number 33292 Answers: 0 Comments: 0

developp f(x)=arctan(x+1) at integr serie

$${developp}\:{f}\left({x}\right)={arctan}\left({x}+\mathrm{1}\right)\:{at}\:{integr}\:{serie} \\ $$

Question Number 33287 Answers: 0 Comments: 0

study the sequence u_(n+1) = (√((1 +u_n )/2)) with 0<u_0 <1 .

$${study}\:{the}\:{sequence}\:\:{u}_{{n}+\mathrm{1}} =\:\sqrt{\frac{\mathrm{1}\:+{u}_{{n}} }{\mathrm{2}}} \\ $$$${with}\:\:\:\:\mathrm{0}<{u}_{\mathrm{0}} <\mathrm{1}\:. \\ $$

Question Number 33285 Answers: 0 Comments: 0

study the sequence u_(n+1) =(√(u_n +(1/(n+1))))

$${study}\:{the}\:{sequence}\:\:{u}_{{n}+\mathrm{1}} \:\:=\sqrt{{u}_{{n}} \:\:\:+\frac{\mathrm{1}}{{n}+\mathrm{1}}} \\ $$

Question Number 33284 Answers: 0 Comments: 0

study the sequence u_(n+1) = ((u_n −ln(1+u_n ))/u_n ^2 ) with u_0 >0 .

$${study}\:{the}\:{sequence}\:\:{u}_{{n}+\mathrm{1}} \:\:=\:\frac{{u}_{{n}} \:−{ln}\left(\mathrm{1}+{u}_{{n}} \right)}{{u}_{{n}} ^{\mathrm{2}} } \\ $$$${with}\:{u}_{\mathrm{0}} >\mathrm{0}\:. \\ $$

Question Number 33282 Answers: 0 Comments: 0

study the sequence u_0 =a>1 and u_(n+1) =(1/2)(u_n +(a/u_n )) .

$${study}\:{the}\:{sequence}\:{u}_{\mathrm{0}} ={a}>\mathrm{1}\:{and} \\ $$$${u}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\left({u}_{{n}} \:+\frac{{a}}{{u}_{{n}} }\right)\:. \\ $$

Question Number 33272 Answers: 1 Comments: 1

The resistance R of an unknown resistor is found by measuring the potential difference V across the resistor and the current I through it and using the equation R=(V/I). The voltmeter reading has a 3% uncertainty and the ammeter reading has a 2% uncertainty. what is the uncertainty in the calculated resistance?

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