Math 234-Calculus II Summer 2020
Lab 9
1 Directions
This lab requires that you have read section 10.7.
Go to https://student.desmos.com and type in this lab's code: RR8 2Z9. If you
are having difficulty with this lab, post a question in the discussion area
below. If you answer a question, give guidance, but not the entire solution.
1.1 Problem 0
Enter your name and SFA email, I need to know who to give the grades to.
1.2 Problem 1
- Define a slider for \(N \in ([0,100] \cap \mathbb{Z})\).
- Define a function \(S(x)\) to be the \(N\)-th partial sum of the Taylor Series expansion of \(\sin(x)\).
- Define a function \(C(x)\) to be the \(N\)-th partial sum of the Taylor Series expansion of \(\cos(x)\).
- Graph \(\sin(x)\) and \(\cos(x)\) as dashed lines, and \(S(x)\) and \(C(x)\) as solid lines. Move the slider for \(N\) and notice how quickly the approximations converge.
- Evaluate \(S(1.1)\) and \(\sin(1.1)\). For what \(N\) is the approximation \(S(1.1)\) equal to \(\sin(1.1)\) for as many digits as desmos is able to show?
1.3 Problem 2
- Define a slider for \(M \in ([0,100] \cap \mathbb{Z})\).
- Define a function \(L(x)\) as the \(M\)-th partial sum of the Taylor Series expansion of \(\ln(x+1)\).
- As you did in Problem 1, can you approximate \(\ln(2)\) in desmos?
- What is the difference between the approximations in Problem 1 and Problem 2?