Hi everyone, having a lot of trouble with Calculus and was wondering if anyone can help.
I have d(t)= -5e^(-5t) x cos(10t)
u = -5e^(-5t)
v = cos(10t)
du/dx = 25e^(-5t)
dv/dx = -10sin10t
duv/dx = 25e^(-5t) x cos(10t) + (-10sin10t) x -5e^(-5t)
= 25e^(-5t)cos(10t) + 50e^(-5t)sin10t
From here I am not sure where to go? Do I have the first bit correct?
0=2 x 1 x 10t
Or do i have to find out tan = sin(a) / cos (a)
If anyone could give me some kicks in the right direction it would be much appreciated, and i can stop wasting paper.
Sorry for not being very clear, yes you are right about the equation equalling zero. The question is to find the Max and min points for a shock absorber rebound .
Once the equation = 0, i have to find the second derivative to measuse the rate of change of the curve, and subistute the x values into the original equation.
Thanks for the help.. If i get stuck again i will post a reply.
I have been looking over your post today and i am a little lost to how you factorized the equation.
The deritive that you stated
25e^(-5t)(cos(10t) + -2sin(20t))
How did you come to this every time i do this i end up with some thing different so i must be factorizing wrong. I would like to know where the 2 and 20 come from seeing that cos(10t) = -10sin(10t)
and the next part of the equation where did the 25e^(-5t) go to as you ended up with
0 = Cos(10t) + 2sin(20t) = tan(10t) = -1/2
When i do it i end up with
0 = Cos(10t) + 2sin(10t) = 2tan(10t)
?Where have i lost my factorizing?
I have attached the graph that i am working from to find the max positive rebound and when it occurs.