Question

Anyone available for a little vector calc help? I have formulas...what I really need is help reducing this thing. I feel like this is elementary yet I'm stuck! Thanks in advance.
I'm finding the moving frame {T,N,B} and computing the curvature and torsion.
x(t)=(e^(2t)sint, e^(2t)cost, 1)
I've got x'(t)=(2e^(2t)sint+e^(2t)cost, 2e^(2t)cost-e^(2t)sint, 0) and that =e^(2t)sint+3e^(2t)cost
Now finding the length of x'(t) is where I get messed up:
||x'(t)|| = sqrt((e^(2t)sint)^2+(3e^(2t)cost)^2)
I have the answer to be sqrt(5)e^(2t) but how on earth do I get to that?

Answer 1

i can help , i use maple for this sort of thing

Answer 2

Thank you - I don't have access to maple at home and for my class I need to show work and do this by hand so I appreciate any help you can give! :)

Answer 3

so this is the function
x(t)=(e^(2t)sint, e^(2t)cost, 1)

Answer 4

yes

Answer 5

one sec, opening maple

Answer 6

how do you upload an image

Answer 7

hows that?

Answer 8

the answer is the bottom of the pic ,

Answer 9

now lets go over how maple got that