Calculus I, Fall 2015

Quiz 1

Oct 06, 2015 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(1 − cos θ)}{tan^{2} θ}.

3. State the Intermediate Value Theorem (Need not prove). Use it to show that x^{x} = 2 has a root.

4. Give formal definition of ‘y = f(x) is continuous at x = c’ in terms of ϵ and δ. Then use the ϵ − δ argument to show that if both f(x) and g(x) are continuous at x = c, then so is f(x) + g(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 2015

Quiz 1

Oct 06, 2015 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(1 − cos θ)}{tan^{2} θ}.

3. State the Intermediate Value Theorem (Need not prove). Use it to show that x^{x} = 2 has a root.

4. Give formal definition of ‘y = f(x) is continuous at x = c’ in terms of ϵ and δ. Then use the ϵ − δ argument to show that if both f(x) and g(x) are continuous at x = c, then so is f(x) + g(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) = ∞