Getting There From Here

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Presentation transcript:

Getting There From Here Limits and Continuity Getting There From Here 1/18/2019 rd

Limit of a Sequence 1 3/2 5/3 7/4 9/5 11/6 … 2 – 1/n, … limit  2 but the sequence does not contain 2. On the other hand the sequence 1 ½ 1 ¾ 1 5/6 1 6/7 …has 1 as a limit and contains 1 1/18/2019 rd

Limit of a Function 1 3/2 5/3 7/4 9/5 11/6 … 2 – 1/n  2 As x  2, f(x) = x2  4 1 9/4 25/9 49/16 81/25 121/36  4 Find limits of 1 ½ 1/3 ¼ 1/5 … 1/n 5 4 11/3 7/2 17/5 … 3 + 2/n ½ ¼ 1/8 1/16 1/32 … 1/18/2019 rd

/2 Some famous limits 1/18/2019 rd

Limit of a Sequence 1 + ½ + ¼ + 1/8 + 1/16 + … (+ 1 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024)  1.999 1/18/2019 rd

Finding a Limit Find 1/18/2019 rd

Limit Find the limits 1/18/2019 rd

L'Hospital's Rule Applies to Indeterminate Forms 1/18/2019 rd

e Evaluate 1/18/2019 rd

Continuity f is continuous at x = a if 1/18/2019 rd