Are you familiar with hyperbolic functions?
I have to eliminate the parameter of:
x=e^(t) + e^(-t)
It has to be Function Y in terms of X.
Everything I do has everything cancel. I can't figure out how to do this. I even tried figuring out what T was in the Y equation, substituting that into the X equation and then getting it in terms of Y. I can't figure it out.
Can someone check the answers I got for these?
Find the EXACT length of C. I got:
L = e^(3) - e^(-3)
Find the EXACT area of the surface obtained by rotating C about the x-axis.
A = 2*Pi*[4e^3 - 1]
I used the formula L = sqrt of [(dx^2) + (dy^2)], which then factored factored into [e^(t) + e^(-t)]... I then put the 3 and 0 in to get the Length. Any mistakes?
For Area, I did the same thing but then multiplied it by 2Pi*Y, which is 2Pi*(6-2t)... I then FOILed and had to integrate: 6e^(t) -te^(t) + 6e^(-t) -te^(-t). I got: 6e^(t) - te^(t) + e^(t) - 6e^(-t) + te^(-t) + te^(-t) and evaluated it from 0 to 3. I got: [6e^3 - 3e^3 + e^3 - 6e^(-3) + 6e^(-3). My final was: [2Pi(4e^3 - 1)]
See any mistakes?