TheoremsDefinitionsProof MethodsProblem Solving Techniques

Catalog of problem solving techniques with examples.

Technique 1. Intermediate Value Theorem

Use the intermediate value theorem to solve problems.

Examples:
Example 1:
Example problem statement\text{Example problem statement}
Technique 2. Extreme Value Theorem

Use the extreme value theorem to solve problems.

Examples:
Example 1:
Example problem statement\text{Example problem statement}
Technique 3. Mean Value Theorem

Use the mean value theorem to solve problems.

Examples:
Example 1:
Example problem statement\text{Example problem statement}
Technique 4. Counterexamples (Dirichlet Function)
Examples:
Example 1:
Give a counterexample.\text{Give a counterexample.}
Technique 5. Chain Rule for FTC 1 (Correlary 7.3.3)
Examples:
Example 1:
Find derivative of F(x)=∫asin(x)cos(t2)dt.\text{Find derivative of } F(x) = \int_a^{sin(x)} cos(t^2)dt.