Calculus I :: Lab 05
Directions
Go to https://student.desmos.com/ and enter the code given in class. Your work saves automatically. You may use your book and notes, and this lab may require some scratch work. Complete the following (there are corresponding slides for each problem):
Problem 0
Enter in your name, I need to know who to give the grades to.
Problem 1
Let \(s(x)=\sin(x)\).
- Graph \(s(x)\).
- Graph the first five derivatives of \(s(x)\).
- Find and graph \(\displaystyle \frac{d^{57}s}{dx^{57}}\).
Problem 2
Repeat Problem 1 but replace \(s(x)\) by \(c(x)\) and \(\sin(x)\) by \(\cos(x)\), so \(c(x)=\cos(x)\).
Problem 3
Let \(f(x) = x^{-1}\). Find and graph the function \(\displaystyle f_k(x) = \frac{d^k f}{dx^k}\), for \(k \in [0,1,2,\ldots 20]\).
Problem 4
Let \(g(x) = xe^x\). Find and graph the function \(\displaystyle g_n(x) = \frac{d^n g}{dx^n}\), for \(n \in [0,1,2,\ldots 30]\).
(Bonus) Problem 5
This is a bonus problem, you will not miss any points if you do not do it.
On Desmos, do problem 58 from section 3.6 of your textbook. You should include the drawing and give the required explanations.