Calculus I, Fall 2014

Quiz 4

Nov 20, 2014 Show all details.

1. Find lim_{x→0}(\frac{1}{x} − \frac{1}{sin x}).

2. Find lim_{x→∞} \frac{e^{x^{2}}}{xe^{x}}.

3. Find the point on y = \sqrt{x}, x ≥ 0 that is closest to (2, 0). Explain why the answer you have is actually a global minimum.

4. Write down Newton’s method that can be used to find \sqrt[3]{2}. Need not give the numerical value.

5. Find ∫ x^{2} + 2^{x} dx.

Calculus I, Fall 2014

Quiz 4

Nov 20, 2014 Show all details.

1. Find lim_{x→0}(\frac{1}{x} − \frac{1}{sin x}).

2. Find lim_{x→∞} \frac{e^{x^{2}}}{xe^{x}}.

3. Find the point on y = \sqrt{x}, x ≥ 0 that is closest to (2, 0). Explain why the answer you have is actually a global minimum.

4. Write down Newton’s method that can be used to find \sqrt[3]{2}. Need not give the numerical value.

5. Find ∫ x^{2} + 2^{x} dx.