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.]

%md yes

yes

Problem alert: Near the end of the video, I discuss a "gear" button in the upper right hand corner. This button no longer exists. Instead, use the "Account" button. I apologize for the error.

Question 1

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

Part a

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

(12+5)/(4-7)

-17/3

Part b

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

4^(2*5-1)-(7+4)

262133

Question 2

Find decimal approximations for the following expressions using Sage.

Part a

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

N(sqrt(5*sin(3^7)))

1.47703673538369

Part b

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

N(log(arcsin(1/3)),2)

-1.0

Part c

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

N(cos(pi/7)-ln(12))

-1.58393778188558

Part d

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

N(1200^(1/8)+2*e^(4/3))

10.0133741057920

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.

f(x)=3*x^2-(5*x)+1

g(t)=((2*t)-1)/((9*t^2)+4)

3*(8)^2-5*8+1

153

f(8)

153

Part c

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

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

%var h

(f(x+h)-f(x))/h

(3*(h + x)^2 - 3*x^2 - 5*h)/h

Part d

Calculate $g(21)$

g(21)

41/3973

Part e

Calculate $g(t-12)$

g(t-12)

(2*t - 25)/(9*(t - 12)^2 + 4)

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.