Math 234-Calculus II Summer 2020
Lab 8
1 Directions
This lab requires that you have read section 10.6.
Go to https://student.desmos.com and type in this lab's code: KUU 5BH. 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
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1.2 Problem 1
- Define a slider for \(N \in ([0,100] \cap \mathbb{Z})\).
- Graph the function \(\displaystyle f(x) = \frac{1}{1-x}\) with domain \((-1,1)\) (since the radius of convergence for the power series of \(f\) is 1).
- Define a function \(F(x)\) to be the first \(N\) terms of the power series for \(f(x)\).
- Play with the slider for \(N\) taking from 0 to the right. Notice that as \(N\) increase the approximation of \(F(x)\) to \(f(x)\) becomes better (converges).
1.3 Problem 2
- Define a slider for \(M \in ([0,100] \cap \mathbb{Z})\).
- Graph the function \(g(x) = e^x\).
- Define a function \(G(x)\) to be the first \(M\) terms of the power series for \(g(x)\).
- What does the radius of convergence for the power series of \(g(x)\) appear to be?