Calculus I, Fall 2014

Quiz 1

Oct 02, 2014 Show all details.

1. Give formal definition of lim_{x→c} f(x) ≠ L (just the definition, need not find ϵ or δ, etc.).

2. Find lim_{θ→0} \frac{sin(sin θ)}{tan 2θ}.

3. State the Intermediate Value Theorem (Need not prove). Use it to find a c such that there is a root of ”x − 1 = cos x” on (c, c + 1).

4. Use the ϵ − δ argument to show that if both f(x) and g(x) are continuous at x = c, then so is 2f(x) − 3g(x).

5. Give formal definitions of the following limits (Just the definition, need not find δ).

(a) lim_{x→c^{−}} f(x) = L (b) lim_{x→−∞} f(x) = ∞

Calculus I, Fall 2014

Quiz 1

Oct 02, 2014 Show all details.

1. Give formal definition of lim_{x→c} f(x) ≠ L (just the definition, need not find ϵ or δ, etc.).

2. Find lim_{θ→0} \frac{sin(sin θ)}{tan 2θ}.

3. State the Intermediate Value Theorem (Need not prove). Use it to find a c such that there is a root of ”x − 1 = cos x” on (c, c + 1).

4. Use the ϵ − δ argument to show that if both f(x) and g(x) are continuous at x = c, then so is 2f(x) − 3g(x).

5. Give formal definitions of the following limits (Just the definition, need not find δ).

(a) lim_{x→c^{−}} f(x) = L (b) lim_{x→−∞} f(x) = ∞