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Question Number 213871 Answers: 0 Comments: 1

Question Number 213862 Answers: 0 Comments: 0

Help me.....!!! :( complex anaylsis problem.. f(z) is entire in path C entire: Differantiable complex function mean f(z) satisfy f(z)=u(x,y)+i∙v(x,y) (∂u/∂x)=−(∂v/∂y) or (∂u/∂y)=−(∂v/∂x) (couchy-riemann) show that ∫_( C) ((f(z))/(f′(z))) dz=2πiΣ_(h=1) ^M P_h −Q_h P_h is number of Zeros in path C Q_h is number of poles in path C and if pole is not exist show that (1/(2πi)) ∫_( C) ((f(z))/(f′(z))) dz this equation is equivalent to the formula for finding the number of zeros f(z)=0

$$\mathrm{Help}\:\mathrm{me}.....!!!\:\::\left(\:\:\right. \\ $$$$\mathrm{complex}\:\mathrm{anaylsis}\:\mathrm{problem}.. \\ $$$${f}\left({z}\right)\:\mathrm{is}\:\mathrm{entire}\:\mathrm{in}\:\mathrm{path}\:{C}\: \\ $$$$\mathrm{entire}:\:\mathrm{Differantiable}\:\mathrm{complex}\:\mathrm{function} \\ $$$$\mathrm{mean}\:{f}\left({z}\right)\:\mathrm{satisfy}\:{f}\left({z}\right)={u}\left({x},{y}\right)+\boldsymbol{{i}}\centerdot{v}\left({x},{y}\right)\:\: \\ $$$$\frac{\partial{u}}{\partial{x}}=−\frac{\partial{v}}{\partial{y}}\:\mathrm{or}\:\:\frac{\partial{u}}{\partial{y}}=−\frac{\partial{v}}{\partial{x}}\:\left(\mathrm{couchy}-\mathrm{riemann}\right) \\ $$$$\mathrm{show}\:\mathrm{that}\:\int_{\:{C}} \:\frac{{f}\left({z}\right)}{{f}'\left({z}\right)}\:\mathrm{d}{z}=\mathrm{2}\pi\boldsymbol{{i}}\underset{{h}=\mathrm{1}} {\overset{{M}} {\sum}}\:{P}_{{h}} −{Q}_{{h}} \\ $$$${P}_{{h}} \:\mathrm{is}\:\mathrm{number}\:\mathrm{of}\:\mathrm{Zeros}\:\mathrm{in}\:\mathrm{path}\:{C}\: \\ $$$${Q}_{{h}} \:\mathrm{is}\:\mathrm{number}\:\mathrm{of}\:\mathrm{poles}\:\mathrm{in}\:\mathrm{path}\:{C} \\ $$$$\mathrm{and}\:\mathrm{if}\:\mathrm{pole}\:\mathrm{is}\:\mathrm{not}\:\mathrm{exist} \\ $$$$\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{2}\pi\boldsymbol{{i}}}\:\int_{\:{C}} \:\frac{{f}\left({z}\right)}{{f}'\left({z}\right)}\:\mathrm{d}{z}\: \\ $$$$\mathrm{this}\:\mathrm{equation}\:\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{formula}\:\mathrm{for}\:\mathrm{finding}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{zeros} \\ $$$${f}\left({z}\right)=\mathrm{0} \\ $$

Question Number 213861 Answers: 1 Comments: 0

Question Number 213859 Answers: 0 Comments: 5

Question Number 213844 Answers: 3 Comments: 0

∫_(−1) ^1 ∫_0 ^(√(1−x^2 )) ∫_(√(x^2 +y^2 )) ^(√(2−x^2 −y^2 )) (√(x^2 +y^2 +z^2 )) dzdydx

$$\:\int_{−\mathrm{1}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \int_{\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }} ^{\sqrt{\mathrm{2}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }} \sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }\:{dzdydx} \\ $$

Question Number 213841 Answers: 1 Comments: 0

Find the vertical asymptots of , f(x)= tan((( π)/(2x + 2)) ) in [ 0 , 4 ] −−−−−−−−−−−−−

$$ \\ $$$$\:\:{Find}\:{the}\:{vertical}\:{asymptots} \\ $$$$\: \\ $$$$\:\:{of}\:\:,\:\:\:{f}\left({x}\right)=\:\mathrm{tan}\left(\frac{\:\pi}{\mathrm{2}{x}\:+\:\mathrm{2}}\:\right)\:\:{in}\: \\ $$$$\: \\ $$$$\:\:\:\:\:\left[\:\mathrm{0}\:\:,\:\:\:\mathrm{4}\:\right] \\ $$$$\:−−−−−−−−−−−−− \\ $$$$ \\ $$

Question Number 213838 Answers: 1 Comments: 1

Question Number 213835 Answers: 1 Comments: 0

Question Number 213821 Answers: 1 Comments: 0

Find: lim_(x→0) (((sinx)/x))^((sinx)/(x − sinx)) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{sinx}}{\mathrm{x}}\right)^{\frac{\mathrm{sinx}}{\mathrm{x}\:−\:\mathrm{sinx}}} \:\:=\:\:? \\ $$

Question Number 213818 Answers: 1 Comments: 1

Question Number 213803 Answers: 2 Comments: 2

Question Number 213802 Answers: 3 Comments: 0

Question Number 213797 Answers: 1 Comments: 0

Question Number 213796 Answers: 4 Comments: 0

Question Number 213817 Answers: 0 Comments: 1

Question Number 213791 Answers: 2 Comments: 2

If x − (x)^(1/3) − (4/( (x)^(1/3) )) = 10 Find (x)^(1/3) − (1/( (x)^(1/3) )) + 3 = ?

$$\mathrm{If}\:\:\:\mathrm{x}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{x}}\:−\:\frac{\mathrm{4}}{\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\:=\:\:\mathrm{10} \\ $$$$\mathrm{Find}\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}\:−\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\:+\:\:\mathrm{3}\:\:=\:\:? \\ $$

Question Number 213790 Answers: 0 Comments: 2

So Weird...... ∫_0 ^( ∞) J_ν (t)e^(−st) dt=(((s+(√(s^2 +1)))^(−ν) )/( (√(s^2 +1)))) J_(−ν) (t)=(−1)^ν J_ν (t) ∫_0 ^( ∞) J_(−ν) (t)e^(−st) dt=(((−1)^ν (s+(√(s^2 +1)))^(−ν) )/( (√(s^2 +1)))) is true But ∫_0 ^( ∞) J_(−ν) (t)e^(−st) dt is not (((s+(√(s^2 +1)))^ν )/( (√(s^2 +1)))) why....? can you explain why Blue equation is not true....

$$\mathrm{So}\:\mathrm{Weird}...... \\ $$$$\int_{\mathrm{0}} ^{\:\infty} {J}_{\nu} \left({t}\right){e}^{−{st}} \mathrm{d}{t}=\frac{\left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{−\nu} }{\:\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}}\: \\ $$$${J}_{−\nu} \left({t}\right)=\left(−\mathrm{1}\right)^{\nu} {J}_{\nu} \left({t}\right)\:\: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:{J}_{−\nu} \left({t}\right){e}^{−{st}} \mathrm{d}{t}=\frac{\left(−\mathrm{1}\right)^{\nu} \left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{−\nu} }{\:\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{is}\:\mathrm{true} \\ $$$$\mathrm{But}\:\int_{\mathrm{0}} ^{\:\infty} \:{J}_{−\nu} \left({t}\right){e}^{−{st}} \mathrm{d}{t}\:\mathrm{is}\:\mathrm{not}\:\frac{\left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{\nu} }{\:\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\mathrm{why}....?\:\mathrm{can}\:\mathrm{you}\:\mathrm{explain}\: \\ $$$$\mathrm{why}\:\mathrm{Blue}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{not}\:\mathrm{true}.... \\ $$

Question Number 213776 Answers: 1 Comments: 0

Find the value of the following expression. Ω= (( Im( Li_2 (2)))/(∫_0 ^( (π/2)) ln(sin(x )) dx)) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{F}{ind}\:\:{the}\:\:{value}\:{of}\:\:{the}\:{following} \\ $$$$\:\:\:\:\:\:\:\:\:\:{expression}. \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\Omega=\:\:\:\frac{\:\mathrm{I}{m}\left(\:\mathrm{Li}_{\mathrm{2}} \:\left(\mathrm{2}\right)\right)}{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\left(\mathrm{sin}\left({x}\:\right)\right)\:{dx}}\:\:=\:? \\ $$

Question Number 213764 Answers: 1 Comments: 0