1. [8 marks] Write your answer to each of the following questions in the space provided. No justification
is necessary.
(a) The graph of the derivative, $f'(x)$, of a function $f(x)$ is given below.
Determine all the values of $x$ on the interval $[-3, 5]$ for which $f$ has a relative minimum.
Answer:
(b) Given that $f$ is a continuous function on the interval $[0, 10]$, and the following:
$\int_0^7 f(x) dx = 5$, $\int_2^7 f(x) dx = 12$, $\int_7^4 f(x) dx = 3$, $\int_7^{10} f(x) dx = 1$
then $\int_0^{10} f(x) dx =$
(c) When evaluating the limit expression $\lim_{x \to a} f(x)^{g(x)}$, which of the following are indeterminate
forms? (Circle your answer(s).)
$1^\infty$ $1^0$ $\infty^0$ $0^0$ $0^\infty$ $\infty^\infty$
(d) $\frac{d}{dx} \int_0^{x^2} \sqrt{1 + t^2} dt =$
(e) $\int_0^{\sqrt{2}} \frac{d}{dx} e^{x^2} dx =$
(f) $\lim_{x \to 1} \frac{\sin(x - 1)}{(x - 1)} = $
