Calc help - verify that x'(0)=y'(0)=0?

Question

For the curves below verify that x'(0)=y'(0)=0 . Determine the derivative dy/dx at the point when t=0.

a.) x(t) = t^3 and y(t) = t^2
b.) x(t) = t^3 and y(t) = t^5
c.) x(t) = t^5 and y(t) = t^3
d.) x(t) = t^(3)-1 and y(t) = 2t^3

I have an exam tomorrow and this was a question on last years sample exam that was posted by my professor without solutions and I don't know how it's done. Please help!!

Answer 1

a)Delta y/ Delta x= 2t delta t/3t^2deta t = 2t/3t^2 and the limit for t==>0 is infinity so the derivative does not exist
b) = 5t^4/3t^2 which has limit 0 for t==>0 so the derivate is 0
c) as a)
d) 6t^2/(-3t^-4) =-2t^6==>0