220 Reputation

15 years, 1 days
Glasgow, United Kingdom

Re:...

What is B, I am confused about it.

Re:...

What is B, I am confused about it.

Re: l'hopital's rule...

Thanks Bro.

The actual expression is

limit(variphi*sigma,sigma=0)=limit(-Ste_liq*((((R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(coth(l*S0)-coth(l))+R3*(1-R1)/sinh(l*S0))*l*cosh((l^2+sigma)^(1/2)*S0)-((R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(coth(l*S0)-coth(l))+R3*(1-R1)/sinh(l*S0))*l*cosh(l*S0)-sigma)/sinh((l^2+sigma)^(1/2)*S0)/S0/sigma*cosh((l^2+sigma)^(1/2)*S0)*(l^2+sigma)^(1/2)+1/sigma/S0*((R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(coth(l*S0)-coth(l))+R3*(1-R1)/sinh(l*S0))*l*(-sinh((l^2+sigma)^(1/2)*S0)*(l^2+sigma)^(1/2)+sinh(l*S0)*l))-1/32*Ste_vap*R1*R4*(6*(R2*l*(R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(-7/6+1/6*cosh(4*l)+cosh(l)^2-1/3*sinh(l)*sinh(3*l))*cosh(l*(-1+S0))+(sinh(l)-1/3*sinh(3*l))*sigma)*((R4*l^2+sigma)/R4)^(1/2)*cosh(((R4*l^2+sigma)/R4)^(1/2)*(-1+S0))-6*(-7/6+1/6*cosh(4*l)+cosh(l)^2-1/3*sinh(l)*sinh(3*l))*(R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(((R4*l^2+sigma)/R4)^(1/2)+l*sinh(((R4*l^2+sigma)/R4)^(1/2)*(-1+S0))*sinh(l*(-1+S0)))*l*R2)/(-1/2+cosh(l)^2-sinh(l)*cosh(l))/(-1+S0)/sigma/sinh(l)^3/sinh(((R4*l^2+sigma)/R4)^(1/2)*(-1+S0))/(cosh(l)^2-1/2+sinh(l)*cosh(l))+(1-R1)*((variphi*sigma+l*R3*coth(l*S0))*coth(l*S0)/(R1*R2*coth(l*(1-S0))+coth(l*S0))-l*R3*coth(l*S0)),sigma=0);

I want to find limit using l'hopital's rule (if desnot work), then i will go for Taylor series.

The reason behind this is to find the expression for the parameter R3.

Thanks

Re: l'hopital's rule...

Thanks Bro.

The actual expression is

limit(variphi*sigma,sigma=0)=limit(-Ste_liq*((((R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(coth(l*S0)-coth(l))+R3*(1-R1)/sinh(l*S0))*l*cosh((l^2+sigma)^(1/2)*S0)-((R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(coth(l*S0)-coth(l))+R3*(1-R1)/sinh(l*S0))*l*cosh(l*S0)-sigma)/sinh((l^2+sigma)^(1/2)*S0)/S0/sigma*cosh((l^2+sigma)^(1/2)*S0)*(l^2+sigma)^(1/2)+1/sigma/S0*((R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(coth(l*S0)-coth(l))+R3*(1-R1)/sinh(l*S0))*l*(-sinh((l^2+sigma)^(1/2)*S0)*(l^2+sigma)^(1/2)+sinh(l*S0)*l))-1/32*Ste_vap*R1*R4*(6*(R2*l*(R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(-7/6+1/6*cosh(4*l)+cosh(l)^2-1/3*sinh(l)*sinh(3*l))*cosh(l*(-1+S0))+(sinh(l)-1/3*sinh(3*l))*sigma)*((R4*l^2+sigma)/R4)^(1/2)*cosh(((R4*l^2+sigma)/R4)^(1/2)*(-1+S0))-6*(-7/6+1/6*cosh(4*l)+cosh(l)^2-1/3*sinh(l)*sinh(3*l))*(R1-1)*(varpi*sigma+l*R3*coth(l*S0))/sinh(l)/(R1*R2*cosh(l*(1-S0))+coth(l*S0)*sinh(l*(1-S0)))*(((R4*l^2+sigma)/R4)^(1/2)+l*sinh(((R4*l^2+sigma)/R4)^(1/2)*(-1+S0))*sinh(l*(-1+S0)))*l*R2)/(-1/2+cosh(l)^2-sinh(l)*cosh(l))/(-1+S0)/sigma/sinh(l)^3/sinh(((R4*l^2+sigma)/R4)^(1/2)*(-1+S0))/(cosh(l)^2-1/2+sinh(l)*cosh(l))+(1-R1)*((variphi*sigma+l*R3*coth(l*S0))*coth(l*S0)/(R1*R2*coth(l*(1-S0))+coth(l*S0))-l*R3*coth(l*S0)),sigma=0);

I want to find limit using l'hopital's rule (if desnot work), then i will go for Taylor series.

The reason behind this is to find the expression for the parameter R3.

Thanks

Re: l'hopital's rule...

Expression is of the form

restart:

A:=0. = limit(.579920000000000000000000000000e-2*((-.9991*(.38*sigma+10*l*coth(.862187887984549593047316871293*l))/sinh(l)/(.7875e-2*cosh(.137812112015450406952683128707*l)+coth(.862187887984549593047316871293*l)*sinh(.137812112015450406952683128707*l))*(coth(.862187887984549593047316871293*l)-coth(l))+9.9910/sinh(.862187887984549593047316871293*l))*l*cosh(.862187887984549593047316871293*(l^2+sigma)^(1/2))-(-.9991*(.38*sigma+10*l*coth(.862187887984549593047316871293*l))/sinh(l)/(.7875e-2*cosh(.137812112015450406952683128707*l)+coth(.862187887984549593047316871293*l)*sinh(.137812112015450406952683128707*l))*(coth(.862187887984549593047316871293*l)-coth(l))+9.9910/sinh(.862187887984549593047316871293*l))*l*cosh(.862187887984549593047316871293*l)-sigma)/sinh(.862187887984549593047316871293*(l^2+sigma)^(1/2))/sigma*cosh(.862187887984549593047316871293*(l^2+sigma)^(1/2))*(l^2+sigma)^(1/2)+.579920000000000000000000000000e-2/sigma*(-.9991*(.38*sigma+10*l*coth(.862187887984549593047316871293*l))/sinh(l)/(.7875e-2*cosh(.137812112015450406952683128707*l)+coth(.862187887984549593047316871293*l)*sinh(.137812112015450406952683128707*l))*(coth(.862187887984549593047316871293*l)-coth(l))+9.9910/sinh(.862187887984549593047316871293*l))*l*(-sinh(.862187887984549593047316871293*(l^2+sigma)^(1/2))*(l^2+sigma)^(1/2)+sinh(.862187887984549593047316871293*l)*l)+.181225000000000000000000000001e-3*(6*(-8.742125*l*(.38*sigma+10*l*coth(.862187887984549593047316871293*l))/sinh(l)/(.7875e-2*cosh(.137812112015450406952683128707*l)+coth(.862187887984549593047316871293*l)*sinh(.137812112015450406952683128707*l))*(-7/6+1/6*cosh(4*l)+cosh(l)^2-1/3*sinh(l)*sinh(3*l))*cosh(.137812112015450406952683128707*l)+(sinh(l)-1/3*sinh(3*l))*sigma)*(1.00000000000000000000000000000*l^2+.563063063063063063063063063063e-2*sigma)^(1/2)*cosh(.137812112015450406952683128707*(1.00000000000000000000000000000*l^2+.563063063063063063063063063063e-2*sigma)^(1/2))+52.452750*(-7/6+1/6*cosh(4*l)+cosh(l)^2-1/3*sinh(l)*sinh(3*l))*(.38*sigma+10*l*coth(.862187887984549593047316871293*l))/sinh(l)/(.7875e-2*cosh(.137812112015450406952683128707*l)+coth(.862187887984549593047316871293*l)*sinh(.137812112015450406952683128707*l))*((1.00000000000000000000000000000*l^2+.563063063063063063063063063063e-2*sigma)^(1/2)+l*sinh(.137812112015450406952683128707*(1.00000000000000000000000000000*l^2+.563063063063063063063063063063e-2*sigma)^(1/2))*sinh(.137812112015450406952683128707*l))*l)/(-1/2+cosh(l)^2-sinh(l)*cosh(l))/sigma/sinh(l)^3/sinh(.137812112015450406952683128707*(1.00000000000000000000000000000*l^2+.563063063063063063063063063063e-2*sigma)^(1/2))/(cosh(l)^2-1/2+sinh(l)*cosh(l))+.9991*(.38*sigma+10*l*coth(.862187887984549593047316871293*l))*coth(.862187887984549593047316871293*l)/(.7875e-2*coth(.137812112015450406952683128707*l)+coth(.862187887984549593047316871293*l))-9.9910*l*coth(.862187887984549593047316871293*l),sigma = 0);

The reason is that I end up with 0/0 form when sigma approches to zero

If you have some thing else in ur mind then plz let me know.

Thanks

Re...

You rightly menstioned the problem. I face the problem to get zero, its worked in some case but no in all cases.

Re...

You rightly menstioned the problem. I face the problem to get zero, its worked in some case but no in all cases.

Re:...

I like your approach, but i want to use newtons method in a loop form, which will also give me the apropriate solution.

The reason for this is that I have no idea about  the interval, bcoz the interval changes with the change in the parameters involved.

if you look into the maple sheet, we have round about 10 parameters.

for example, if i consider R3 to be positive then i expect that the interval of study will be positive, when S0 (another parameter)  is 1/2.

But for every parameter i cant guess it.

Thanks

Re:...

I like your approach, but i want to use newtons method in a loop form, which will also give me the apropriate solution.

The reason for this is that I have no idea about  the interval, bcoz the interval changes with the change in the parameters involved.

if you look into the maple sheet, we have round about 10 parameters.

for example, if i consider R3 to be positive then i expect that the interval of study will be positive, when S0 (another parameter)  is 1/2.

But for every parameter i cant guess it.

Thanks

Re...

i need the simplist form of the expression with out assuming to cut it in parts.

As u suggested that we can use "shorthand" notations, but I am afried to disagree with you.

I am looking for the more compress form of the equation. I am send you the another file plz see it

Re...

i need the simplist form of the expression with out assuming to cut it in parts.

As u suggested that we can use "shorthand" notations, but I am afried to disagree with you.

I am looking for the more compress form of the equation. I am send you the another file plz see it

Re...

Thanks for your kind and quick responce

It worek very well but if u have some other commands to make my solution more compressed and simplified, then plz tell me

Re...

Thanks for your kind and quick responce

It worek very well but if u have some other commands to make my solution more compressed and simplified, then plz tell me

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