Unit 16 – Day 4 Name: Date: Integrated Analysis: NOTES
Functions and Limits – Finding Limits Algebraically
Theorems: Limit of a Constant Function:
Limit of the Identity Function (𝑥):
Ex 1) lim
𝑥→35 = ______ Ex 2) lim
𝑥→3𝑥 = ______
Theorems: Limit of a Sum: Limit of a Difference:
Ex 3) lim
𝑥→−3(𝑥 + 4) = Ex 4) lim
𝑥→4(6 − 𝑥) =
Theorems: Limit of a Product: Limit of a Quotient:
Ex 5) lim
𝑥→5(−4𝑥) = Ex 6) lim
𝑥→63𝑥
=
Unit 16 – Day 4 Recall our answers from each of the first six examples… You should notice something about these limits that will make these theorems much easier. Ex 1) lim
𝑥→35 = 𝟓 Ex 2) lim
𝑥→3𝑥 = 𝟑 Ex 3) lim
𝑥→−3(𝑥 + 4) = 𝟏
Ex 4) lim
𝑥→4(6 − 𝑥) = 𝟐 Ex 5) lim
𝑥→5(−4𝑥) = −𝟐𝟎 Ex 6) lim
𝑥→63𝑥
= 𝟏𝟐
This should not be surprising if you remember what limits are used to be able to accomplish. We use them to find what the value would be a discontinuous function.
One Last Theorem: Limit of a Function: Ex 7) lim
𝑥→5(2𝑥2 − 5𝑥 − 10) = Ex 8) lim
𝑥→1(3𝑥3 + 4𝑥 − 2) =
The six theorems on the front of the paper are not meaningless though. Here is why… Try the next two examples by substituting in the value for 𝑐. What happens? What can we do different? Ex 9) lim
𝑥→3𝑥2−𝑥−6
𝑥2−9= Ex 10) lim
𝑥→05𝑥−sin 𝑥
𝑥=
