Question

Sa se calculeze curbura curbei c(t) = (3t^2, 3t − t^3) in punctul P(t = 1).

Answer 1

Răspuns:

c(t)=(3t²,3t-t³) P t=1

{x(t)=3t²

{y(t)=3t-t³

x`(t)=6t

x``(t)=6

y`(t)=3-3t²

y``(t)= -6t

k=[-6t*6t-6(3-3t²)]/[(6t)²+(3-3t²)²]^(3/2)=

(-36t²-18+18t²)/(36t²+9-6t²+81t⁴)^(3/2)=

(-18t²-18)/(81t⁴+30t²+9)^(3/2)=k

k(1)=(-18*1-18)/(81*1+30*1+9)^(3/2)=

-36/(81+30+9)^(3/2)=

-36/120^(3/2)=

-36/120*√120=

-3/5*2√30=-3/10√30

Explicație pas cu pas: