calc 3 help
find curvature k of the curve y=e^(-x) at x=1

Question

calc 3 help
find curvature k of the curve y=e^(-x) at x=1

anonymous · Answer

would I just find the first and 2nd derivative and do y''/(1+y^2)^3/2 ?

anonymous · Answer

isn't the tangent vector just the first derivative and the speed S just the magnitude of the first derivative?

anonymous · Answer

curvature is not the magnitude of the tangent vector divided by the speed

anonymous · Answer

anyone know the curvature formula when I'm only given an equation for y? I know how to do it if I'm given equations for both x and y, but not when it's only y

anonymous · Answer

mathteacher is right, that;s is ONE of the many curvature formulas, I'm looking at it in my notes right now

mathteacher1729 · Answer

@myko you are correct -- I apologize. It is the mangnitude of the DERIVATIVE of the tangent vector ... divided by speed. :( My apologies everyone.

mathteacher1729 · Answer

Here is where that definition is derived and explained: pg 4 PDF http://cfsv.synechism.org/c2/sec23.pdf

anonymous · Answer

would I be able to cross product the first and 2nd derivative, find the magnitude of the cross product, and then divide it by the magnitude of the first derivative cubed?

anonymous · Answer

||r'Xr''|| / ||r'||^3?

anonymous · Answer

that is one of the formulas for curvature I have in my notes

zarkon · Answer

$$\kappa = \frac{|y''|}{(1+y'^2)^{3/2}}$$

zarkon · Answer

how about that

anonymous · Answer

I also have that one, would it matter which one I use?

zarkon · Answer

no...but since you are given y as a function of x I would think the above formula might be the nicest

anonymous · Answer

the |y"| is that the absolute value of y" or magnitude?

zarkon · Answer

abs

zarkon · Answer

y'' is just a function of x...not a vector valued function

anonymous · Answer

Yeah I asked about that formula in my first post on this question, but without the | |

and no one brought it up or commented about it

zarkon · Answer

ah..ic

zarkon · Answer

it should have the abs

anonymous · Answer

yeah, I just didn't know how to do the | |, just found out how to do the bars now haha

zarkon · Answer

gotcha :)

zarkon · Answer

you also forgot a ' on the y in the denominator

anonymous · Answer

-e^(-x) squared

is just e^-2x correct?

zarkon · Answer

yes

anonymous · Answer

this thing is just filled with fractions within fractions -.-

zarkon · Answer

it shouldn't be too bad

anonymous · Answer

yeah, just gonna punch in the values into the calculator

anonymous · Answer

I like the what seems to be a Data picture