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Relation and FunctionsQuestion and Answers: Page 12

Question Number 142871 Answers: 0 Comments: 0

determine arctan(x+iy) at form u(x,y)+iv(x,y)

$$\mathrm{determine}\:\mathrm{arctan}\left(\mathrm{x}+\mathrm{iy}\right)\:\mathrm{at}\:\mathrm{form}\:\mathrm{u}\left(\mathrm{x},\mathrm{y}\right)+\mathrm{iv}\left(\mathrm{x},\mathrm{y}\right) \\ $$

Question Number 142869 Answers: 2 Comments: 0

calculate ∫_(−∞) ^(+∞) ((x^2 dx)/((x^2 −x+3)^2 ))

$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 142430 Answers: 2 Comments: 0

calculate ∫_0 ^∞ ((log^2 x)/(1+x^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 142429 Answers: 1 Comments: 0

calculate U_n =∫_0 ^∞ ((log^n x)/(1+x^n ))dx find nature of the serie ΣU_n

$${calculate}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{{n}} {x}}{\mathrm{1}+{x}^{{n}} }{dx} \\ $$$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma{U}_{{n}} \\ $$

Question Number 142426 Answers: 1 Comments: 0

find the value of ∫_0 ^∞ ((xlogx)/((1+x^3 )^2 ))dx

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{xlogx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 142425 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((log^3 x)/(1+x^3 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{\mathrm{3}} {x}}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 142424 Answers: 0 Comments: 0

2)calculate Σ_(k=1) ^(n−1) sin(((kπ)/n)) (n>2) 1) use Rieman sum to prove that ∫_0 ^π log(sinx)dx=−πlog2

$$\left.\mathrm{2}\right){calculate}\:\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{{k}\pi}{{n}}\right)\:\:\:\left({n}>\mathrm{2}\right) \\ $$$$\left.\mathrm{1}\right)\:{use}\:{Rieman}\:{sum}\:{to}\:{prove} \\ $$$${that}\:\int_{\mathrm{0}} ^{\pi} {log}\left({sinx}\right){dx}=−\pi{log}\mathrm{2} \\ $$

Question Number 142423 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ ((log^2 x)/(1+x^2 ))dx

$${study}\:{the}\:{convergence}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 142389 Answers: 1 Comments: 0

∫(e^x /(cosx))dx

$$\int\frac{{e}^{{x}} }{{cosx}}{dx} \\ $$

Question Number 142365 Answers: 1 Comments: 0

calculate ∫ (√(1+e^x +e^(2x) ))dx

$$\mathrm{calculate}\:\int\:\:\sqrt{\mathrm{1}+\mathrm{e}^{\mathrm{x}} \:+\mathrm{e}^{\mathrm{2x}} }\mathrm{dx} \\ $$

Question Number 142115 Answers: 2 Comments: 0

simplify A_n (x)=(1+ix)^n +(1−ix)^n x from C

$$\mathrm{simplify}\:\:\mathrm{A}_{\mathrm{n}} \left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{ix}\right)^{\mathrm{n}} +\left(\mathrm{1}−\mathrm{ix}\right)^{\mathrm{n}} \:\:\:\mathrm{x}\:\mathrm{from}\:\mathrm{C} \\ $$

Question Number 142021 Answers: 0 Comments: 0

simplfy f(x)=tan(α arcsinx) and g(x)=tan(α arcosx) α is real x∈[−1,1]

$$\mathrm{simplfy}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{tan}\left(\alpha\:\mathrm{arcsinx}\right) \\ $$$$\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{tan}\left(\alpha\:\mathrm{arcosx}\right)\:\:\alpha\:\mathrm{is}\:\mathrm{real} \\ $$$$\mathrm{x}\in\left[−\mathrm{1},\mathrm{1}\right] \\ $$

Question Number 141935 Answers: 0 Comments: 0

Determine if the numbers 1, 5, 8 are in the range of the fuctions f(x)= { ((2x if −2≤x<2)),((3 if x=2)) :}

$${Determine}\:{if}\:{the}\:{numbers}\:\mathrm{1},\:\mathrm{5},\:\mathrm{8}\: \\ $$$${are}\:{in}\:{the}\:{range}\:{of}\:{the}\:{fuctions} \\ $$$$ \\ $$$${f}\left({x}\right)=\begin{cases}{\mathrm{2}{x}\:\:\:\:\:\:{if}\:\:−\mathrm{2}\leqslant{x}<\mathrm{2}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:{if}\:\:\:\:{x}=\mathrm{2}}\end{cases} \\ $$$$ \\ $$

Question Number 141933 Answers: 0 Comments: 1

let f(t) =∫_0 ^∞ ((logx)/(x^2 +t^2 ))dx (t>0) 1)calculate f^((n)) (t) and f^((n)) (0) 2) developp f at integr serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{t}^{\mathrm{2}} }\mathrm{dx}\:\:\:\left(\mathrm{t}>\mathrm{0}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{t}\right)\:\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$

Question Number 141932 Answers: 2 Comments: 0

calculate lim_(x→0) ((sin(sin(sinx))+1−cos(x^2 ))/x^3 )

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{sin}\left(\mathrm{sin}\left(\mathrm{sinx}\right)\right)+\mathrm{1}−\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 141775 Answers: 1 Comments: 0

find ∫_0 ^∞ (e^(−x^2 ) /((x^2 +3)^2 ))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 141774 Answers: 2 Comments: 0

calculate ∫_0 ^∞ (e^(−x^2 ) /(1+x^2 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 142229 Answers: 1 Comments: 0

deveopp g(x)=(1/(sin(nx))) at fourier series (x≠((kπ)/n))

$$\mathrm{deveopp}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{nx}\right)}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{series}\:\left(\mathrm{x}\neq\frac{\mathrm{k}\pi}{\mathrm{n}}\right) \\ $$

Question Number 142228 Answers: 1 Comments: 0

developpf(x)=(2/(3+cosx)) at fourier serie

$$\mathrm{developpf}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\mathrm{3}+\mathrm{cosx}}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 142231 Answers: 0 Comments: 0

find ∫ ((ch(x))/(cosx))dx

$$\mathrm{find}\:\int\:\frac{\mathrm{ch}\left(\mathrm{x}\right)}{\mathrm{cosx}}\mathrm{dx} \\ $$

Question Number 141653 Answers: 0 Comments: 0

what is condition to have log( I +A)=Σ a_n A^n and determine the sequence (a_n ) A ∈ M_n (C)

$${what}\:{is}\:{condition}\:{to}\:{have} \\ $$$${log}\left(\:{I}\:+{A}\right)=\Sigma\:{a}_{{n}} {A}^{{n}} \\ $$$${and}\:{determine}\:{the}\:{sequence}\:\left({a}_{{n}} \right) \\ $$$${A}\:\in\:{M}_{{n}} \left({C}\right) \\ $$

Question Number 141652 Answers: 0 Comments: 0

A = (((1 2)),((−1 1)) ) find e^(A ) and e^(tA) find ch(A) and sh(A)

$${A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\\{−\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$${find}\:{e}^{{A}\:} \:{and}\:{e}^{{tA}} \\ $$$${find}\:{ch}\left({A}\right)\:{and}\:{sh}\left({A}\right) \\ $$

Question Number 141937 Answers: 0 Comments: 2

Write and graph the equation of the graph of y=sin(πx) It is stretched up by a factor of 5 and shifted (1/2) unit to the right Help me please

$${Write}\:{and}\:{graph}\:{the}\:{equation}\:{of}\:{the}\:{graph}\:{of}\:{y}={sin}\left(\pi{x}\right) \\ $$$${It}\:{is}\:{stretched}\:{up}\:{by}\:{a}\:{factor}\:{of}\:\mathrm{5}\:{and}\:{shifted}\:\frac{\mathrm{1}}{\mathrm{2}}\:{unit}\:{to}\:{the}\:{right} \\ $$$${Help}\:{me}\:{please} \\ $$$$ \\ $$

Question Number 141570 Answers: 1 Comments: 0

Question Number 141551 Answers: 0 Comments: 3

Question Number 141568 Answers: 0 Comments: 2

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