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Project: Aurora Stefoff - Calculus 1 Lab Fall 2023

Path: 02 - Intro to Jupyter Notebooks/Intro to Jupyter Notebooks Assignment.ipynb

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Introduction to Jupyter Notebooks Assignment

Question 1

[1 point] Compute the following using CoCalc (all the numbers in the question should appear in your answer - don't simplify in your head). Make sure you have enough parentheses to get the order of operations right.

Part a

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

In [6]:

(12+5)/(4-7)

Out[6]:

-17/3

In [0]:

Part b

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

In [9]:

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

Out[9]:

262141

In [0]:

Question 2

[4 points] Find decimal approximations for the following expressions using CoCalc.

[Hint: Use the N() command to convert to decimal -- N stands for "numerical approximation"]

Part a

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

In [10]:

sqrt(5*sin(3^7))

Out[10]:

sqrt(5)*sqrt(sin(2187))

Part b

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

In [17]:

log(2)*(arcsin(1/3))

Out[17]:

arcsin(1/3)*log(2)

In [0]:

Part c

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

In [30]:

cos(pi/7)-ln(12)

Out[30]:

cos(1/7*pi) - log(12)

In [0]:

Part d

ParseError: KaTeX parse error: Double superscript at position 3: ^4^̲4\displaystyle\…

In [34]:

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

Out[34]:

  Cell In [34], line 1
    sqrt[Integer(8)]{Integer(1200)}+(Integer(2))cdot e**{Integer(4)/Integer(3)}
                    ^
SyntaxError: invalid syntax

Question 3

[5 points] Consider the functions

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

g(t)=\frac{2t-1}{9t^2+4}

Part a

Define $f$ and $g$ . Don't forget you need explicit multiplications and parentheses for the fraction in g(t).

In [40]:

f(x)=3*x^2-5*x+1
g(t)= (2*t-1)/(9*t^2+4)

Part b

Calculate $f(8)$

In [43]:

f(8)

Out[43]:

153

Part c

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

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

In [48]:

h=1
(f(x+1)-f(x))/1

Out[48]:

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

Part d

Calculate $g(21)$

In [49]:

g(21)

Out[49]:

41/3973

Part e

Calculate $g(t-12)$

In [50]:

g(t-12)

Out[50]:

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

In [0]:

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Introduction to Jupyter Notebooks Assignment

Question 1

Part a

Part b

Question 2

Part a

Part b

Part c

Part d

Question 3

Part a

Part b

Part c

Part d

Part e

Product

Resources

Company

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more, all in one place. Commercial Alternative to JupyterHub.

Introduction to Jupyter Notebooks Assignment

Question 1

Part a

Part b

Question 2

Part a

Part b

Part c

Part d

Question 3

Part a

Part b

Part c

Part d

Part e

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place. Commercial Alternative to JupyterHub.