Question

Curvature

Answer 1

When. To use |T'(t)|/|r'(t)| and this |r'(t)| x r''(t)|/|r'(t)|^3

Answer 2

@Loser66

Answer 3

Both are the formulas of the curvature but got confused when to implement them

Answer 4

Not sure what you mean :)

Answer 5

For instance find the curvature r(t) = <t,t^2,t^3> at the point (1,1,1)

Answer 6

I got the answer

Answer 7

But why can't we use the 1eqyation

Answer 8

r'(t) = <1,2t, 3t^2>
r"(t) =<0,2,6t>
cross them to get <6t^2,-6t,2>

Answer 9

My prof said that sometime this way is more convenient: K(x) = \(\dfrac{|f"(x)|}{(1+(f'(x))^2)^3/2}\)

Answer 10

if we are given y = f(x) directly, not a parametric equation

Answer 11

We flexibly use one of them. No need to worry. Like derivative, we can find by limit but why , right? when using theorem is much more convenient

Answer 12

but my question is in paramtric form

Answer 13

u said to use \[|r'(t)| X |r''(t)|/|r'(t)|^3\]

Answer 14

because it is convenient?

Answer 15

yes.

Answer 16

you see, just derivatives