Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1663

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?

$${The}\:\boldsymbol{{resistance}}\:\boldsymbol{{R}}\:\boldsymbol{{of}}\:\boldsymbol{{an}}\: \\ $$$$\boldsymbol{{unknown}}\:\boldsymbol{{resistor}}\:\boldsymbol{{is}}\:\boldsymbol{{found}}\:\boldsymbol{{by}} \\ $$$$\boldsymbol{{measuring}}\:\boldsymbol{{the}}\:\boldsymbol{{potential}} \\ $$$$\boldsymbol{{difference}}\:\boldsymbol{{V}}\:\boldsymbol{{across}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{resistor}}\:\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{current}}\:\boldsymbol{{I}}\:\boldsymbol{{through}} \\ $$$$\boldsymbol{{it}}\:\boldsymbol{{and}}\:\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{equation}}\:\boldsymbol{{R}}=\frac{{V}}{{I}}. \\ $$$$\boldsymbol{{The}}\:\boldsymbol{{voltmeter}}\:\boldsymbol{{reading}}\:\boldsymbol{{has}}\:\boldsymbol{{a}}\:\mathrm{3\%} \\ $$$$\boldsymbol{{uncertainty}}\:\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{ammeter}} \\ $$$$\boldsymbol{{reading}}\:\boldsymbol{{has}}\:\boldsymbol{{a}}\:\mathrm{2\%}\:\boldsymbol{{uncertainty}}. \\ $$$$\boldsymbol{{what}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{uncertainty}}\:\boldsymbol{{in}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{calculated}}\:\boldsymbol{{resistance}}? \\ $$

Question Number 33271    Answers: 0   Comments: 0

For a couple of weeks now.Two men have been missing here . Please come around.We so much enjoy everyone′s presence.

$${For}\:{a}\:{couple}\:{of}\:{weeks}\:{now}.{Two} \\ $$$${men}\:{have}\:{been}\:{missing}\:{here}\:. \\ $$$${Please}\:{come}\:{around}.{We}\:{so}\:{much} \\ $$$${enjoy}\:{everyone}'{s}\:{presence}. \\ $$

Question Number 33270    Answers: 0   Comments: 15

For a couple of weeks now.Two men have been missing here . Please come around.We so much enjoy everyone′s presence.

$${For}\:{a}\:{couple}\:{of}\:{weeks}\:{now}.{Two} \\ $$$${men}\:{have}\:{been}\:{missing}\:{here}\:. \\ $$$${Please}\:{come}\:{around}.{We}\:{so}\:{much} \\ $$$${enjoy}\:{everyone}'{s}\:{presence}. \\ $$

Question Number 33267    Answers: 1   Comments: 1

12 men can make 24 articles in 6 days. How many articles can 3 men make in 3 days?

$$\mathrm{12}\:\mathrm{men}\:\mathrm{can}\:\mathrm{make}\:\mathrm{24}\:\mathrm{articles}\:\mathrm{in}\:\mathrm{6}\:\mathrm{days}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{articles}\:\mathrm{can}\:\mathrm{3}\:\mathrm{men}\:\mathrm{make}\:\mathrm{in} \\ $$$$\mathrm{3}\:\mathrm{days}? \\ $$

Question Number 33259    Answers: 0   Comments: 1

find the value of ∫_0 ^∞ ((arctan(2x))/(a^2 +x^2 )) dx with a≠0

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }\:{dx}\:{with}\:{a}\neq\mathrm{0} \\ $$

Question Number 33258    Answers: 0   Comments: 0

if (1/(1+cosx)) = (a_0 /2) +Σ_(n≥1) a_n cos(nx) calculate a_0 and a_n

$${if}\:\:\:\frac{\mathrm{1}}{\mathrm{1}+{cosx}}\:=\:\frac{{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{{n}\geqslant\mathrm{1}} {a}_{{n}} {cos}\left({nx}\right)\:{calculate}\:{a}_{\mathrm{0}} \\ $$$${and}\:{a}_{{n}} \\ $$

Question Number 33257    Answers: 0   Comments: 1

let g(x)= (1/(1+x^4 )) 1) find g^((n)) (x) 2) calculate g^((n)) (0) 3) if g(x)=Σ u_n x^n find the sequence u_n

$${let}\:{g}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{g}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{if}\:{g}\left({x}\right)=\Sigma\:{u}_{{n}} \:{x}^{{n}} \:\:\:{find}\:{the}\:{sequence}\:{u}_{{n}} \\ $$

Question Number 33256    Answers: 0   Comments: 1

let f(x) = (1/(1+x^2 )) 1) calculate f^((n)) (x) 2) find f^((n)) (0) 3) developp f(x) at integr serie.

$${let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie}. \\ $$$$ \\ $$

Question Number 33255    Answers: 0   Comments: 2

if the roots of the equation 3x^2 +5x+2=0 are (α+β)(αβ) then the value of p if x^2 + px − 6=0 is?

$${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$$\:\:\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}=\mathrm{0}\:{are}\:\left(\alpha+\beta\right)\left(\alpha\beta\right) \\ $$$${then}\:{the}\:{value}\:{of}\:{p}\:{if}\:{x}^{\mathrm{2}} +\:{px}\:−\:\mathrm{6}=\mathrm{0} \\ $$$${is}? \\ $$

  Pg 1658      Pg 1659      Pg 1660      Pg 1661      Pg 1662      Pg 1663      Pg 1664      Pg 1665      Pg 1666      Pg 1667   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com