Calculating Limits Using The Limit Laws Dec 21 2020 nbsp 0183 32 In the previous section we evaluated limits by looking at graphs or by constructing a table of values In this section we establish laws for calculating limits and learn how to apply these laws
This theorem allows us to calculate limits by squeezing a function with a limit at a point a that is unknown between two functions having a common known limit at a Figure 2 27 illustrates this idea Decide if the following limits exist and if a limit exists nd its value 1 lim x 1 x 4 2x3 x2 3 Since this is a polynomial function we can calculate the limit by direct substitution lim x 1 x4
Calculating Limits Using The Limit Laws
Calculating Limits Using The Limit Laws
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Calculating limits by testing values of x close to a is tedious The following Theorem essentially says that any nice combination of functions has exactly the limit you d expect Theorem Lecture 4 Section 2 3 Calculating Limits Using the Limit Laws 4 3 There are other algebraic techniques such as combining rational expressions with common denominators and
In this section we will develop some rules that will help us quickly and accurately compute limits Theorem Limit Laws Let ff and gg be functions cc a constant and a n Ra n R Suppose lim x af x Llim x af x L and lim x In this section we use the following properties of limits called the Limit Laws to calculate limits The limit of a sum is the sum of the limits The limit of a difference is the difference of the limits
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2 3 Calculating Limits Using The Limit Laws
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Sep 9 2015 nbsp 0183 32 Ms Roshan s AP Calculus AB Videos Based on Stewart s Calculus Concepts amp Contexts0 00 Introduction0 24 The Limit Laws1 16 Example 14 42 Further Limit Pro The limit laws allow us to evaluate limits of functions without having to go through step by step processes each time For polynomials and rational functions You can evaluate the limit of a function by factoring and canceling by multiplying by
Evaluate the limit and justify each step by indicating the appropriate Limit Laws by plugging in x 1 into the function If f x g x when x a then provided the limits exist x 2 Calculate x Use the Squeeze Theorem to show that lim x2 cos 20 x 0 4 Use the graphs below to evaluate each of the following limits If the limit does not exist explain why
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Section 2 3 Calculating Limits Using The Limit Laws
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Calculating Limits Using The Limit Laws - In this section we use the following properties of limits called the Limit Laws to calculate limits The limit of a sum is the sum of the limits The limit of a difference is the difference of the limits