mat 3749 introduction to analysis section 2.3 part i derivatives
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MAT 3749Introduction to Analysis
Section 2.3 Part I
Derivatives
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Differentiable implies continuous Something else
References
Section 2.3
HW
Do not use ε-δ.
Derivatives
Example 1
Theorem
Analysis: Step 1
Analysis
Analysis
Analysis
Analysis
Analysis
Analysis
Analysis
Analysis
Analysis
Analysis
Proof
Proof
Proof
Proof
Remark
The converse of the last theorem is false
Example 2
Give a counterexample of the converse of the last theorem.
The Derivative as a Function
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.
Example 3
2
sin2
lim
2x
x
x
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