Calculus I, Fall 2015

Quiz 4

Nov 26, 2015

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

2. 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.

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

4. Express ∫_{1}^{2} \frac{1}{1 + x^{2}} dx as a limit of Riemann sum (with uniformly spaced partition

and c_{k} of your choice). Then find the limit of the definite integral using fundamental Theorem of Calculus.

5. Evaluate \frac{d}{dx} ∫_{x^{2}}^{0} \sqrt{1 + t^{4}} dt.

Calculus I, Fall 2015

Quiz 4

Nov 26, 2015

Show all details.

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

2. 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.

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

4. Express ∫_{1}^{2} \frac{1}{1 + x^{2}} dx as a limit of Riemann sum (with uniformly spaced partition

and c_{k} of your choice). Then find the limit of the definite integral using fundamental Theorem of Calculus.

5. Evaluate \frac{d}{dx} ∫_{x^{2}}^{0} \sqrt{1 + t^{4}} dt.