Definition: The tangent line to the curve y=f(x), at the point P=(a,f(a)),
is given by the line through P, with slope

m = lim_x->a (f(x)-f(a))/(x-a)

if it exists! Consequently, the equation of the line is given by:

y - f(a) = m*(x-a) An alternate form of the slope is given by

m = lim _h->0 [f(a+h)-f(a)]/h

Definition: The tangent line to a parameterized curve r(t) = < x(t),y(t) >
is given by L(t) = r(a) + tv, where v s the tangent vector to r at t=a, that is,

v = lim _t->a [r(t)-r(a)]/(t-a)

Average velocity is defined as net displacement over time.

Average speed is defined as total displacement over time.

Instantaneous velocity is given by

v(a) = lim _h->0 [f(a+h)-f(a)]/h

Instantaneous vector velocity is given by

v(a) = lim _h->0 [r(a+h)-r(a)]/h

If y depends on x, then the ratio

delta y / delta x = [y₂-y₁]/(x₂-x₁) is called the average rate of change of y, with respect to x over the interval [x₂,x₁].

Last modified Sun Sep 15 14:43:42 CDT 1996