mat 3749 introduction to analysis section 2.3 part i derivatives
TRANSCRIPT
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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 ε-δ.
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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
2
sin2
lim
2x
x
x
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Classwork