# Question:Taylor series

## Question:Taylor series

Maple

Hi,

I tried to find the limit of the following equation using l'hopital's rule, when sigma approches to zero find i couldn't find it.

Now i want to use Taylor series to find the limit of the following equation, when sigma approches zero.

Q:=(((-1+R1)*(l*(-1+S0)*R3*R2^2*R1^2*(cosh(l*S0)*sigma*S0*sinh(l*S0)+l*Ste1*cosh(l*S0)^2-l*Ste1)*cosh(l*(-1+S0))^2+(l*(R2*R1*Ste2*S0*variphi*R4-(-1+S0)*(R3*S0-Ste1*variphi))*sigma*cosh(l*S0)^2+(R2*R1*Ste2*S0*l^2*R3*R4-(-1+S0)*(-sigma^2*S0*variphi+Ste1*l^2*R3))*sinh(l*S0)*cosh(l*S0)-l*(R2*R1*Ste2*S0*R4+Ste1*(-1+S0))*variphi*sigma)*R2*sinh(l*(-1+S0))*R1*cosh(l*(-1+S0))-((R2*R1*Ste2*l^2*R3*R4+variphi*sigma^2*(-1+S0))*S0*cosh(l*S0)+l*(R2*R1*Ste2*S0*R4+Ste1*(-1+S0))*variphi*sinh(l*S0)*sigma)*sinh(l*(-1+S0))^2*cosh(l*S0))*sinh((l^2+sigma)^(1/2)*S0)-((R2^2*(-sigma*cosh(l*S0)^2+l*sinh(l*S0)*R3*(-1+R1)*cosh(l*S0)+sigma)*R1^2*cosh(l*(-1+S0))^2-(l*R3*(-1+R1)*cosh(l*S0)-sigma*sinh(l*S0)*(-variphi+R1*variphi+2))*R2*sinh(l*(-1+S0))*cosh(l*S0)*R1*cosh(l*(-1+S0))-sigma*cosh(l*S0)^2*sinh(l*(-1+S0))^2*(-variphi+1+R1*variphi))*cosh((l^2+sigma)^(1/2)*S0)-(-1+R1)*(R1*R2*cosh(l*(-1+S0))*sinh(l*S0)-cosh(l*S0)*sinh(l*(-1+S0)))*(R3*R2*cosh(l*(-1+S0))*l*R1+sigma*variphi*sinh(l*(-1+S0))))*Ste1*(-1+S0)*(l^2+sigma)^(1/2))*sinh((R4*(l^2*R4+sigma))^(1/2)/R4*(-1+S0))-sinh((l^2+sigma)^(1/2)*S0)*(((((variphi-1)*R1-variphi)*sigma*cosh(l*S0)^2+l*sinh(l*S0)*R3*(-1+R1)*cosh(l*S0)-((variphi-1)*R1-variphi)*sigma)*R2^2*R1*cosh(l*(-1+S0))^2-(l*R3*(-1+R1)*cosh(l*S0)+sinh(l*S0)*((variphi-2)*R1-variphi)*sigma)*R2*sinh(l*(-1+S0))*cosh(l*S0)*cosh(l*(-1+S0))-sigma*cosh(l*S0)^2*sinh(l*(-1+S0))^2)*cosh((R4*(l^2*R4+sigma))^(1/2)/R4*(-1+S0))-(-1+R1)*R2*(R2*R1*(-variphi*sigma+variphi*sigma*cosh(l*S0)^2+sinh(l*S0)*l*R3*cosh(l*S0))*cosh(l*(-1+S0))-cosh(l*S0)*sinh(l*(-1+S0))*(variphi*sigma*sinh(l*S0)+l*R3*cosh(l*S0))))*R1*S0*(R4*(l^2*R4+sigma))^(1/2)*Ste2)/sinh((l^2+sigma)^(1/2)*S0)/(R1*R2*cosh(l*(-1+S0))*sinh(l*S0)-cosh(l*S0)*sinh(l*(-1+S0)))^2/sigma/S0/(-1+S0)/sinh((R4*(l^2*R4+sigma))^(1/2)/R4*(-1+S0));

Plz help me out

Thanks

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