1. Limits:
Definition: A limit is the value a function or sequence approaches as the variable within that
function gets nearer and nearer to a particular value.
For example, the limit of f(x) is L as
Average Rate of Change: The average rate of change of a function f(x) over an interval between
two points (a, f(a) and (b, f(b) is the slope of the secant line connecting the two points.
To calculate
Velocity and Acceleration:
Derivatives can relate to physics very easily.
If a function gives the position of something as a function of time, the first derivative gives its
velocity, and the second d
Part 2:
Limits:
1
Easy:
Evaluate:
5 x2 +6 x +4
)
lim
Simple Plug In
x 1
5 x2 +6 x +4
lim
x 1
=5+6+4
= 15
2
Medium:
x
( 203 x )(e 20 3 e)
xe
lim
x e
f ( x )f (a)
The limit of this difference quotien
Integrals:
1 Easy:
( x 22 x ) dx=
3
1
This question involves using the basic power rule for antidifferentiation and then correctly
substituting the endpoints and evaluating:
x3
27
1
4
2
x
9 1 =
3
3
3