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Kernel: SageMath 10.0

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

12+54−7\displaystyle\frac{12+5}{4-7}

(12+5)/(4-7)
-17/3

Part b

42×5−1−(7+4)\displaystyle 4^{2\times 5-1}-(7+4)

4^((2*5)-1)-7+4
262141

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

5sin⁡(37)\displaystyle \sqrt{5\sin(3^7)}

sqrt(5*sin(3^7))
sqrt(5)*sqrt(sin(2187))

Part b

log⁡2(arcsin⁡(13))\displaystyle\log_{2}\left(\arcsin\left(\frac{1}{3}\right)\right)

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

Part c

cos⁡(π7)−ln⁡(12)\displaystyle \cos\left(\frac{\pi}{7}\right)-\ln(12)

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

Part d

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

^4 sqrt[8]{1200}+2cdot e^{4/3}
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)=3x2−5x+1f(x)=3x^2-5x+1g(t)=2t−19t2+4g(t)=\frac{2t-1}{9t^2+4}

Part a

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

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

Part b

Calculate f(8)f(8)

f(8)
153

Part c

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

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

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

Part d

Calculate g(21)g(21)

g(21)
41/3973

Part e

Calculate g(t−12)g(t-12)

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