Differential and Integral Calculus (21-120) — Feedback on Homework 2

Homework 2 was due on Thursday 5th September 2013 and consisted of:

The questions I marked were 2.2/12 (out of 2), 2.2/34 (out of 2), 2.3/18 (out of 2) and 2.4/20 (out of 3). Everyone got 1 free point for submitting their homework.

Section 2.2 Q12. Common errors included:

Section 2.2 Q34. The main reason why people didn't get both points on this question was failing to justify the answer. If you wrote $\lim_{x \to \pi^-} \cot x = -\infty$ then you'll have got one point. The second point was reserved for justification. I'd have been happy with a graph, or an argument along the lines that, as $x$ approaches $\pi$ from below, $\cos x$ approaches $-1$ and $\sin x$ approaches $0$ from above. Since dividing $-1$ by a small positive number gives a large negative number, the limit is $-\infty$. (Note that as $x \to \pi^+$ the opposite happens: you divide by a small negative number, and so $\lim_{x \to \pi^+} \cot x = +\infty$.)

Section 2.3 Q18. There were two common mistakes on this question:

Section 2.4 Q20. This question was bound to be a challenge! Of the people who found a correct value of $\delta$ (anything in the region $0 \lt \delta \le \frac{5}{4}\varepsilon$ was acceptable), the most common issue was not proving that the value of $\delta$ worked. Partial credit was given for working which was readable and had reversible steps. Other issues included:

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