Calculus I, Fall 2013

Quiz 5

Dec 26, 2013 Show all details.

1. Find the solutions of \frac{dy}{dx} = 2x\sqrt{1 − y^{2}} (−1 < y < 1).

2. Evaluate ∫ sin x tanh(cos x)dx

3. True or False? Explain.

(ln(ln x))^{2} = o(x) as x → ∞.

4. Evaluate ∫ cos \sqrt{x} dx

5. Evaluate ∫ \frac{π}{2} ; \frac{π}{3} \frac{sin^{2} x}{\sqrt{1 − cos x}}dx

Calculus I, Fall 2013

Quiz 5

Dec 26, 2013 Show all details.

1. Find the solutions of \frac{dy}{dx} = 2x\sqrt{1 − y^{2}} (−1 < y < 1).

2. Evaluate ∫ sin x tanh(cos x)dx

3. True or False? Explain.

(ln(ln x))^{2} = o(x) as x → ∞.

4. Evaluate ∫ cos \sqrt{x} dx

5. Evaluate ∫ \frac{π}{2} ; \frac{π}{3} \frac{sin^{2} x}{\sqrt{1 − cos x}}dx