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Question Number 28202 Answers: 1 Comments: 1

Question Number 28201 Answers: 0 Comments: 0

prove the sine rule using dot product need help please

$$\mathrm{prove}\:\mathrm{the}\:\mathrm{sine}\:\mathrm{rule}\:\mathrm{using}\:\mathrm{dot}\:\mathrm{product} \\ $$$$\mathrm{need}\:\mathrm{help}\:\mathrm{please} \\ $$

Question Number 28143 Answers: 1 Comments: 0

x−(1/x)=3 x^2 −(1/x^2 )=?

$$\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{3} \\ $$$$\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=? \\ $$

Question Number 28124 Answers: 0 Comments: 3

f(R^+ →R) is a differentiable function obeying 2f(x)=f(xy)+f((x/y)) for all x,y ∈ R^+ and f(1)=0, f ′(1)=1 . Find f(x). More questions may follow..

$${f}\left({R}^{+} \rightarrow{R}\right)\:{is}\:{a}\:{differentiable} \\ $$$${function}\:{obeying} \\ $$$$\mathrm{2}{f}\left({x}\right)={f}\left({xy}\right)+{f}\left(\frac{{x}}{{y}}\right) \\ $$$${for}\:{all}\:{x},{y}\:\in\:{R}^{+} \:{and}\: \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{0},\:{f}\:'\left(\mathrm{1}\right)=\mathrm{1}\:. \\ $$$${Find}\:{f}\left({x}\right).\:{More}\:{questions}\:{may} \\ $$$${follow}.. \\ $$

Question Number 28116 Answers: 0 Comments: 0

Question Number 28105 Answers: 0 Comments: 1

Question Number 28098 Answers: 1 Comments: 0

lim_(x→∞) ((log_e x)/x^h ) , h > 0

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{log}_{\mathrm{e}} \mathrm{x}}{\mathrm{x}^{\mathrm{h}} }\:,\:\:\:\:\:\:\:\:\:\:\:\mathrm{h}\:>\:\mathrm{0} \\ $$

Question Number 28097 Answers: 0 Comments: 3

lim_(x→∞) ((3^x − 2^x )/x^2 )

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}^{\mathrm{x}} \:−\:\mathrm{2}^{\mathrm{x}} }{\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 28096 Answers: 0 Comments: 2

lim_(x→∞) (x^2 /(x − sinx))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}\:−\:\mathrm{sinx}} \\ $$

Question Number 28095 Answers: 0 Comments: 2

lim_(x→0^− ) (1 + tanx)^(−cotx)

$$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\mathrm{tanx}\right)^{−\mathrm{cotx}} \\ $$

Question Number 28093 Answers: 0 Comments: 2

lim_(x→0^− ) (1 + tanx)^(cotx)

$$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\mathrm{tanx}\right)^{\mathrm{cotx}} \\ $$

Question Number 28113 Answers: 1 Comments: 1

Question Number 28110 Answers: 0 Comments: 1

Question Number 28088 Answers: 0 Comments: 6

lim_(x→0^+ ) (sinx)^((tanx))

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\:\left(\mathrm{sinx}\right)^{\left(\mathrm{tanx}\right)} \\ $$

Question Number 28084 Answers: 0 Comments: 6

lim_(x→∞) (x − log_e x)

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\left(\mathrm{x}\:−\:\mathrm{log}_{\mathrm{e}} \mathrm{x}\right) \\ $$

Question Number 28076 Answers: 1 Comments: 1

Question Number 28075 Answers: 0 Comments: 0

Question Number 28073 Answers: 0 Comments: 1

find ∫_0 ^1 e^(−2x) ln(1+t e^(−x) )dx with 0<t<1 .

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+{t}\:{e}^{−{x}} \right){dx}\:\:\:{with}\:\:\mathrm{0}<{t}<\mathrm{1}\:\:. \\ $$

Question Number 28072 Answers: 0 Comments: 1

let give the function f(x)=x^4 2π periodic and even developp f atfourier series.

$${let}\:{give}\:{the}\:{function}\:\:{f}\left({x}\right)={x}^{\mathrm{4}} \:\:\:\mathrm{2}\pi\:{periodic}\:{and}\:{even} \\ $$$${developp}\:\:\:{f}\:{atfourier}\:{series}. \\ $$

Question Number 28071 Answers: 0 Comments: 3

let give A_p = ∫_0 ^π t^p cos(nx) with nand p from N 1) find a relation between A_p and A_(p−2) 2) find arelation between A_(2p) and A_(2p−2) 3) find a relation?betweer A_(2p+1) and A_(2p−1) 3) cslculat A_(0 ) , A_1 , A_2 , A_2 .

$${let}\:{give}\:\:{A}_{{p}} =\:\int_{\mathrm{0}} ^{\pi} \:{t}^{{p}} \:{cos}\left({nx}\right)\:\:{with}\:{nand}\:{p}\:{from}\:{N} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{relation}\:{between}\:\:{A}_{{p}} \:{and}\:{A}_{{p}−\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{arelation}\:{between}\:\:{A}_{\mathrm{2}{p}} \:\:{and}\:{A}_{\mathrm{2}{p}−\mathrm{2}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{a}\:{relation}?{betweer}\:{A}_{\mathrm{2}{p}+\mathrm{1}} \:{and}\:\:{A}_{\mathrm{2}{p}−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{cslculat}\:\:{A}_{\mathrm{0}\:} ,\:{A}_{\mathrm{1}} ,\:{A}_{\mathrm{2}} \:,\:{A}_{\mathrm{2}} . \\ $$

Question Number 28070 Answers: 1 Comments: 0

Question Number 28068 Answers: 0 Comments: 0

let give I_a = ∫_0 ^(+∝) (t^(a−1) /(1+t))dt by using Residus theorem find the value of I_a with 0<a<1 .

$${let}\:{give}\:\:\:{I}_{{a}} \:\:=\:\:\int_{\mathrm{0}} ^{+\propto} \:\:\:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt}\:\:\:{by}\:{using}\:{Residus}\:{theorem} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{I}_{{a}} \:\:\:\:\:{with}\:\:\mathrm{0}<{a}<\mathrm{1}\:\:\:. \\ $$

Question Number 28067 Answers: 0 Comments: 0

let give f(x)= (1/(2+cosx)) fonction 2π periodic even. developp f at fourier series.

$${let}\:{give}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}+{cosx}}\:\:\:{fonction}\:\mathrm{2}\pi\:{periodic}\:{even}. \\ $$$${developp}\:{f}\:\:{at}\:{fourier}\:{series}. \\ $$

Question Number 28050 Answers: 0 Comments: 14

Question Number 28044 Answers: 0 Comments: 8

Question Number 28041 Answers: 0 Comments: 0

∫(ϰ^2 /((ϰsinϰ+cosϰ)^2 ))d(ϰ)

$$\int\frac{\varkappa^{\mathrm{2}} }{\left(\varkappa\mathrm{sin}\varkappa+\mathrm{cos}\varkappa\right)^{\mathrm{2}} }\mathrm{d}\left(\varkappa\right) \\ $$

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