Question

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)} = $

          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)} = $

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:
∫0^7 f(x) dx = 5, ∫2^7 f(x) dx = 12, ∫7^4 f(x) dx = 3, ∫7^10 f(x) dx = 1
then ∫0^10 f(x) dx =
(c) When evaluating the limit expression limx → a f(x)^g(x), which of the following are indeterminate
forms? (Circle your answer(s).)
1^∞ 1^0 ∞^0 0^0 0^∞ ∞^∞
(d) (d)/(dx)∫0^x^2√(1 + t^2) dt =
(e) ∫0^√(2)(d)/(dx) e^x^2 dx =
(f) limx → 1(sin(x - 1))/((x - 1)) =

Added by Paul L.

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