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Question Number 36009 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((xdx)/((2x+1+i)^3 )) with i^2 =−1 .

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{xdx}}{\left(\mathrm{2}{x}+\mathrm{1}+{i}\right)^{\mathrm{3}} }\:\:{with}\:{i}^{\mathrm{2}} \:=−\mathrm{1}\:. \\ $$

Question Number 35990 Answers: 0 Comments: 2

calculate ∫_2 ^5 ((xdx)/(2x+1 +(√(x−1))))

$${calculate}\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\:\frac{{xdx}}{\mathrm{2}{x}+\mathrm{1}\:+\sqrt{{x}−\mathrm{1}}} \\ $$

Question Number 35988 Answers: 1 Comments: 2

let f(x) = ((x+2)/(x^3 −4x +3)) 1) calculate f^((n)) (x) 2) developp f at integr serie.

$${let}\:{f}\left({x}\right)\:=\:\frac{{x}+\mathrm{2}}{{x}^{\mathrm{3}} −\mathrm{4}{x}\:+\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 35987 Answers: 0 Comments: 4

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

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

Question Number 35986 Answers: 0 Comments: 5

let f(x)= (√(1 +n x^2 )) −nx +3 with n integr 1) calculate lim_(x→+∞) and lim_(x→−∞) f(x) 2) calculate f^′ (x) 3) give the equation of assymptote of f at point A(1,f(1)) . 4)calculate lim_(x→+∞) ((f(x))/x) and lim_(x→−∞) ((f(x))/x) .

$${let}\:{f}\left({x}\right)=\:\sqrt{\mathrm{1}\:+{n}\:{x}^{\mathrm{2}} }\:\:\:−{nx}\:+\mathrm{3}\:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \:{and}\:{lim}_{{x}\rightarrow−\infty} {f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{the}\:{equation}\:{of}\:{assymptote}\:{of}\:{f}\:{at} \\ $$$${point}\:\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right)\:. \\ $$$$\left.\mathrm{4}\right){calculate}\:{lim}_{{x}\rightarrow+\infty} \:\frac{{f}\left({x}\right)}{{x}}\:{and}\:{lim}_{{x}\rightarrow−\infty} \:\:\frac{{f}\left({x}\right)}{{x}}\:. \\ $$

Question Number 35983 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((2(√t) +1)/(t^5 +3))dt .

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{\mathrm{2}\sqrt{{t}}\:+\mathrm{1}}{{t}^{\mathrm{5}} \:\:\:+\mathrm{3}}{dt}\:\:. \\ $$

Question Number 35982 Answers: 0 Comments: 0

let f(t) =∫_0 ^∞ e^(−arctsn( 1+tx^2 )) dx with t from R 1) calculate f^′ (t) 2) find a simple form of f(t) .

$${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−{arctsn}\left(\:\mathrm{1}+{tx}^{\mathrm{2}} \right)} {dx}\:\:{with}\:{t}\:{from}\:{R} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right)\:. \\ $$

Question Number 36003 Answers: 2 Comments: 0

x [(2),(1) ]+y [(3),(5) ]+ [((−8)),((−11)) ]=0 find x and y

$${x}\begin{bmatrix}{\mathrm{2}}\\{\mathrm{1}}\end{bmatrix}+{y}\begin{bmatrix}{\mathrm{3}}\\{\mathrm{5}}\end{bmatrix}+\begin{bmatrix}{−\mathrm{8}}\\{−\mathrm{11}}\end{bmatrix}=\mathrm{0} \\ $$$${find}\:{x}\:{and}\:{y} \\ $$

Question Number 35968 Answers: 2 Comments: 1

Question Number 35960 Answers: 0 Comments: 3

Solve using Residue Theorem I = ∫_(−∞) ^(+∞) (x^2 /(x^4 + 16)) dx

$$\mathrm{Solve}\:\mathrm{using}\:\mathrm{Residue}\:\mathrm{Theorem} \\ $$$$\mathrm{I}\:=\:\int_{−\infty} ^{+\infty} \:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} \:+\:\mathrm{16}}\:{dx} \\ $$

Question Number 35951 Answers: 1 Comments: 3

(cosθ+cosβ/sinθ−sinβ)=(sinθ+sinβ/cosθ−cosβ) prove ghis

$$\left({cos}\theta+{cos}\beta/{sin}\theta−{sin}\beta\right)=\left({sin}\theta+{sin}\beta/{cos}\theta−{cos}\beta\right)\:{prove}\:{ghis} \\ $$

Question Number 35949 Answers: 1 Comments: 1

∫_0 ^( α) ((tan θ)/(√(a^2 cos^2 θ−b^2 sin^2 θ))) dθ = ?

$$\int_{\mathrm{0}} ^{\:\:\alpha} \frac{\mathrm{tan}\:\theta}{\sqrt{{a}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta−{b}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta}}\:{d}\theta\:=\:? \\ $$

Question Number 35940 Answers: 1 Comments: 1

Question Number 35939 Answers: 1 Comments: 0

lim_(x→4) ( ((asin (x−4) + cos πx −1)/(x−4)) )^((x−2)/(x−3)) = 4 Find ′a′ ?

$$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\:\left(\:\frac{{a}\mathrm{sin}\:\left({x}−\mathrm{4}\right)\:+\:\mathrm{cos}\:\pi{x}\:−\mathrm{1}}{{x}−\mathrm{4}}\:\right)^{\frac{{x}−\mathrm{2}}{{x}−\mathrm{3}}} =\:\mathrm{4} \\ $$$${Find}\:'{a}'\:? \\ $$

Question Number 35933 Answers: 1 Comments: 0

differentiate from the first principle y=(1/(√x))

$$\boldsymbol{\mathrm{differentiate}}\:\boldsymbol{\mathrm{from}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{principle}} \\ $$$$\boldsymbol{\mathrm{y}}=\frac{\mathrm{1}}{\sqrt{\boldsymbol{{x}}}} \\ $$

Question Number 35920 Answers: 1 Comments: 1

∫ ((e^(2x) +1)/(2e^x −1)) dx = ?

$$\int\:\frac{{e}^{\mathrm{2}{x}} +\mathrm{1}}{\mathrm{2}{e}^{{x}} −\mathrm{1}}\:{dx}\:=\:? \\ $$

Question Number 35915 Answers: 1 Comments: 0

if P(A) and P(B) are independent events then P(A∣B)=??

$${if}\:{P}\left({A}\right)\:{and}\:{P}\left({B}\right)\:{are}\:{independent} \\ $$$${events}\:{then}\:{P}\left({A}\mid{B}\right)=?? \\ $$

Question Number 35909 Answers: 1 Comments: 4

∫((7x−6)/((x^2 +25)(√((x−3)^2 +4)))) dx = ?

$$\int\frac{\mathrm{7}{x}−\mathrm{6}}{\left({x}^{\mathrm{2}} +\mathrm{25}\right)\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{4}}}\:{dx}\:=\:? \\ $$

Question Number 35899 Answers: 0 Comments: 2

Evaluate log_(√2) 4+log_(1/2) 16−log_4 32

$${Evaluate}\:{log}_{\sqrt{\mathrm{2}}} \mathrm{4}+{log}_{\mathrm{1}/\mathrm{2}} \mathrm{16}−{log}_{\mathrm{4}} \mathrm{32} \\ $$

Question Number 35897 Answers: 0 Comments: 2

log_x^(1/2 ) 64=3. What is x?

$${log}_{{x}^{\mathrm{1}/\mathrm{2}\:} } \mathrm{64}=\mathrm{3}.\:{What}\:{is}\:{x}? \\ $$

Question Number 35895 Answers: 2 Comments: 1

Question Number 35892 Answers: 2 Comments: 2

Question Number 35886 Answers: 1 Comments: 0

Question Number 35882 Answers: 0 Comments: 4

An open pipe 40cm long and a closed pipe 32cm long,with the same diameter,sound the same fundamental frequency in unison. Find the end correction of these pipes.

$${An}\:{open}\:{pipe}\:\mathrm{40}{cm}\:{long}\:{and}\:{a} \\ $$$${closed}\:{pipe}\:\mathrm{32}{cm}\:{long},{with}\:{the} \\ $$$${same}\:{diameter},{sound}\:{the}\:{same} \\ $$$${fundamental}\:{frequency}\:{in}\:{unison}. \\ $$$${Find}\:{the}\:{end}\:{correction}\:{of}\:{these} \\ $$$${pipes}. \\ $$

Question Number 35881 Answers: 1 Comments: 1

A train travelling at 30m/s , approaching a stationary observer emits a tone at a frequency of 480Hz. If the speed of sound is 330m/s, determine the frequency of the note the observer hears.

$${A}\:{train}\:{travelling}\:{at}\:\mathrm{30}{m}/{s}\:, \\ $$$${approaching}\:{a}\:{stationary}\:{observer} \\ $$$${emits}\:{a}\:{tone}\:{at}\:{a}\:{frequency}\:{of}\:\mathrm{480}{Hz}. \\ $$$${If}\:{the}\:{speed}\:{of}\:{sound}\:{is}\:\mathrm{330}{m}/{s}, \\ $$$${determine}\:{the}\:{frequency}\:{of}\:{the} \\ $$$${note}\:{the}\:{observer}\:{hears}. \\ $$

Question Number 35880 Answers: 0 Comments: 0

Determine the intensity level of 12 people′s speech,if each person speaks with an intensity level of 60dB

$${Determine}\:{the}\:{intensity}\:{level}\:{of} \\ $$$$\mathrm{12}\:{people}'{s}\:{speech},{if}\:{each}\:{person} \\ $$$${speaks}\:{with}\:{an}\:{intensity}\:{level}\:{of} \\ $$$$\mathrm{60}{dB} \\ $$

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