Presentation exercises are marked with a *.
Section 2.1: Exercises 14, 15, 22, 24, 25*
Section 2.2: Exercises 27*,28
Section 2.3 Exercises 1,2,4,22
Do exercises 4-8 on this algebra review sheet.
Learn to use Mathematica as a scientific calculator by working through this tutorial.
Then do the following exercises (to be handed in). First open the template notebook which you prepared last week. Save a copy of it called numerical_derivative.nb. Do your work in this saved copy. Change the title to "Numerical calculation of the derivative." Follow the example at the end of the tutorial (the section called numerical calculation of the derivative) to calculate the approximate value of the derivatives of the following functions at the indicated points:
1. Calculate the derivative of f(x) = x^3 at x = 2.
2. Calculate the derivative of f(x) = exp(x^2) at x = 1.5. The Mathematica notation for exp(x^2) is Exp[x^2].
3. Calculate the derivative of f(x) = ln(x) at x = 2. Recall that the Mathematica notation for ln(x) is Log[x].
Print out your finished notebook and hand it in with the rest of your homework.
This one is a presentation exercise! You calculated the derivative of f(x) = x^3 at x =2 numerically and approximately in Mathematica Exercise 1. Now calculate the derivative f'(2) exactly by considering the average rate of change (1/h) (f(2 + h) - f(2)) with h as a variable, simplifying, and then taking the limit as h -> 0. Find the derivative f'(a) for an arbitrary value of a in the same way.