Review of Sage Assignment.sagews

Review Assignment

Question 0

Watch the lecture video here.

Did you watch the video? [Type yes or no.]

Question 1

Consider the function $\displaystyle f(x)=\frac{9x^3-2}{x^2+7x}$.

Part a

Graph this function using the window $-5\le x \le 5$ and $-10\le y\le 10$.

Part b

Compute $\displaystyle\lim_{x\to-7^+}f(x)$.

Part c

Compute $f'(x)$.

Part d

Compute $f'(3)$.

Part e

Compute $\displaystyle\int f(x)\, dx$.

Part f

Compute $\displaystyle\int_1^4 f(x)\, dx$.

Question 2

Suppose the function $v(t)=8t^2-2t+1$ gives the velocity at time $t$ of a particle travelling in a straight line.

Part a

If the particle starts out at position $0$ when $t=0$, find the function $p(t)$ that gives the position of the particle at time $t$.

Part b

Find the function $a(t)$, which gives the acceleration of the particle at time $t$.

Part c

Graph $p$, $v$, and $a$ on the same axes with $0\le t\le 4$, using different colors and/or line styles for each.

This material was developed by Aaron Tresham at the University of Hawaii at Hilo and is
licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.