Additional Examples from Section 3.1
- Find
the slope of the tangent to the curve
at x = 2.
= 
Option: Simplify this complex fraction by multiplying both numerator and denominator by (x+1)(3).
= 
Simplify the numerator, but leave the denominator in factored form.
= 
= 
- The
displacement of a particle (in meters) of an object moving in a straight
line is given by
, where t is measured in seconds.
(a) Find the instantaneous velocity (v), at t = a.
(b) Find the instantaneous velocity (v), at t = 1.
(a) 
Distribute:
Combine Like Terms:
Multiply by 
to eliminate complex
fraction:
Factor out the h in the numerator
Simplify
Take the limit (plug in h = 0)
(b) If t = 1, then 
- Carefully review example 3 on page 115 of your text.