MAT 1234 Calculus I Section 1.6 Part I Using the Limit Laws

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Presentation transcript:

MAT 1234 Calculus I Section 1.6 Part I Using the Limit Laws

HW Homework 1.6 Part I Do your HW ASAP. Tutoring is available!!! Seriously, Do not wait.

Quiz Friday and … Quiz :1.6 Part I (2 problems from your HW) Make sure you have an approved calculator.

Recall Limit of the following form is important 1.4: Estimate limits by tables 1.6: Compute limits by algebra 1.5: Formally define limits

Preview Limit Laws Direct Substitution Property Practical summary of all the limit laws

Limit Laws 11 limit laws that help us to compute limits (printed on p.5). Foundation of computing limits, but tedious to use. Practical methods will be introduced.

Limit Laws 7.

Limit Laws 8.

Limit Laws If and exist, then

Example 1

Limit Laws 1. If and exist, then Why the assumption above is important?

Example Find

Direct Substitution Property

Why? Polynomials are “continuous” functions x y a

Why? Polynomials are “continuous” functions

Why? Polynomials are “continuous” functions

Example 1 (Polynomial)

Remark 1 Once you substitute in the number, you do not need the limit sign anymore.

3 is in the domain of the rational function

Direct Substitution Property

Limit Laws Summary

Example 3

Q&A

Example 4 (Simplify)

1.Use equal signs 2.Use parentheses for expressions with sums and differences of more than 1 term. 3. Show the substitution step. Expectations: Standard Notations and Presentation

4. Do not actually “cross out” terms.

Remark 1 Again Once you substitute in the number, you do not need the limit sign anymore.

Example 5 (Combine the terms)

Remark 1 Again (What? Again!) Once you substitute in the number, you do not need the limit sign anymore.

Example 7 (Multiply by conjugate)

Review of conjugates

Example 7 (Multiply by conjugate)

Review: We learned… Limit Laws Direct Substitution Property of polynomials and rational functions Techniques Simplify Combine the terms Multiply by conjugate

Classwork Use pencils Use “=“ signs Do not “cross out” anything. Do not skip steps Once you substitute in the number, you do not need the limit sign anymore.

I Do not Know my Algebra.... What to do? What would Jesus do?