Intro to Sage Assignment.sagews

Introduction to Sage Assignment

Note 1: Below each question, click on the horizontal gray line. This will create a new input cell. Type your answer directly into this Sage worksheet, and click "Run."

Note 2: If you opened the PDF, please open the .sagews file and put your answers there.

Question 0

Watch the lecture video here.

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

Question 1

Compute the following in Sage. Make sure you have enough parentheses to get the order of operations right.

Part a

$\displaystyle\frac{12+5}{4-7}$

Part b

$\displaystyle 4^{2\times 5-1}-(7+4)$

Question 2

Find decimal approximations for the following expressions using Sage.

Part a

$\displaystyle \sqrt{5\sin(3^7)}$

Part b

$\displaystyle\log_{2}\left(\arcsin\left(\frac{1}{3}\right)\right)$

Part c

$\displaystyle \cos\left(\frac{\pi}{7}\right)-\ln(12)$

Part d

$\displaystyle\sqrt[8]{1200}+2\cdot e^{4/3}$

Question 3

Consider the functions

$$f(x)=3x^2-5x+1$$$$g(t)=\frac{2t-1}{9t^2+4}$$

Part a

Define $f$ and $g$ in Sage. Don't forget you need explicit multiplications, and use plenty of parentheses.

Part b

Calculate $f(8)$

Part c

Calculate $\displaystyle\frac{f(x+h)-f(x)}{h}$

[Hint: don't forget to declare $h$ to be a variable]

Part d

Calculate $g(21)$

Part e

Calculate $g(t-12)$

Notes

• Each lab assignment is worth 5 points.

• The assignment will be graded in class, although you may choose to work on the assignment before class.

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.