1. Test 1: Limit of a Function
Calculate the slope of a secant to curve using the formula:
𝑚= 𝑓 𝑏 −𝑓(𝑎) 𝑏−𝑎
Calculate the slope of the tangent to curve at 𝑥=𝑎 using the formula:
lim ℎ→0 𝑓 𝑎+ℎ −𝑓(𝑎) ℎ
Solve real life applications involving rates of change:
Average rate of change = slope of the secant.
Instantaneous rate of change = slope of the tangent.

2. Test 1: Limit of a Function
Given the graph of a function, I can:
Find the value of the function at a particular spot on the domain, i.e. 𝑓 2 .
Find lim 𝑥→ 𝑎 − 𝑓 𝑥 (the left sided limit) and lim 𝑥→ 𝑎 + 𝑓 𝑥 (the right sided limit) and use this to determine the existence and value of lim 𝑥→𝑎 𝑓 𝑥 .
Use this information to determine continuity at a point.
Given the equation of a function, I can:
Find the value of the function at a particular spot on the domain, i.e. 𝑓 2 .
Find lim 𝑥→ 𝑎 − 𝑓 𝑥 (the left sided limit) and lim 𝑥→ 𝑎 + 𝑓 𝑥 (the right sided limit) and use this to determine the existence and value of lim 𝑥→𝑎 𝑓 𝑥 .
Use this information to determine continuity at a point.

3. Test 1: Limit of a Function
Calculate the limit algebraically, when it exists using:
Direct substitution (polynomial functions).
Factoring (rational functions) – trinomials, difference of squares/cubes, grouping, etc.
Rationalizing the numerator and/or the denominator using the conjugate.
Substitution – i.e. let 𝑢=( 𝑥+4) →𝑥= 𝑢 3 −4 , don’t forget to change the limiting value.
Exploring the right and left sided limits of piecewise functions, including absolute value.
Sketch the graph of a function given details of the function, i.e. :
The value of the function at particular points.
Limiting values.
Details about direction and/or continuity.

4. Review Questions
Review P.56 – 59 #1, 2ac, 3, 4, 6abd, 7, 8, 9, 11, 15c, 17, 18abc, 19a
Practice Test P.60 #3, 6, 7, 8