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### Chapter 3

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### The Limit of a Sequence

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### 3 DIFFERENTIATION

2014 1 29 May 25 2011 SECTION 3.1 Definition of the Derivative 103 In Exercises 11–14 refer to Figure 12 1 2 3 5 4 x y FIGURE 12 Graph of f x 11 Determine f a for a = 1 2 4 7 solution Remember that the value of the derivative of f at x = a can be interpreted as the slope of the line tangent to the graph of y = f x at x = a.From Figure 12 we see that the graph of y = f x is a

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### 3 DIFFERENTIATION

2014 1 29 May 25 2011 SECTION 3.1 Definition of the Derivative 103 In Exercises 11–14 refer to Figure 12 1 2 3 5 4 x y FIGURE 12 Graph of f x 11 Determine f a for a = 1 2 4 7 solution Remember that the value of the derivative of f at x = a can be interpreted as the slope of the line tangent to the graph of y = f x at x = a.From Figure 12 we see that the graph of y = f x is a

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Use the graph to estimate lim x → − 3 f x Step 1 Examine the limit from the left Step 2 Examine the limit from the right Step 3 The one sided limits are the same so the limit exists Answer lim x → − 3 f x ≈ 2 Example 3.

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