Essay Questions

Calculus I

Date

Question

9-5 Explain the ε-δ definition of limits.
9-12 Explain the proof of the product rule.
9-19 Explain why the derivative of cos(x) is -sin(x).
Use the methods in § 3.5.
9-26 Explain the proof of the chain rule.
10-3 Explain: if f has a local maximum at c, then either
1) f '(c)=0, or
2) f '(c) doesn't exist, or
3) c is an endpoint.
10-10 Explain horizontal asymptotes intuitively.
Also, explain the precise definition of a limit as x appoaches ±∞.
10-31 Explain the definition of the definite integral.
Go through an example that helps you understand this definition.
11-7 Explain the proof of the Fundamental Theorem of Calculus.
11-14 Explain the shell method for finding volumes.
11-23 Explain what exponential functions are,
and why the derivative of ex is ex.
11-30 Why is the integral of 1/x equal to
the natural logarithm of the absolute value of x (plus C)?
12-9 Explain L'Hospital's rule.
Why do we need the conditions that f(x) and g(x) both tend to 0 as x tends to a?