MAT 3749 Introduction to Analysis

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MAT 3749Introduction to Analysis

• Section 2.3 Part I
• Derivatives

http//myhome.spu.edu/lauw
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Preview

• Differentiable implies continuous
• Something else

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References

• Section 2.3

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HW

• Do not use e-d.

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Derivatives
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Example 1
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Theorem
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Analysis Step 1
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Analysis
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Analysis
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Analysis
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Analysis
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Analysis
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Analysis
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Analysis
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Analysis
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Analysis
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Analysis
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Proof
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Proof
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Proof
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Proof
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Remark

• The converse of the last theorem is false

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Example 2

• Give a counterexample of the converse of the last
  theorem.

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The Derivative as a Function
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Change of Variables in Limits

• Change of variables is a technique you have
  used frequently to evaluate limits in a
  completely natural way.
• To formulate this technique formally and justify
  it rigorously, however, is a task requiring some
  subtlety.

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Example 3
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Classwork