ASSIGNMENT 1·10 for SECTION 001
There are two parts to this assignment. The first part is online at www.mathxl.com. The second part
consists of the questions on this page. You are expected to provide full solutions with complete arguments
and justifications. You will be graded on the correctness, clarity and elegance of your solutions. Your answers
must be typeset or very neatly written. They must be stapled, with your name and student number at the top
of each page.
1. Solve the equation xx
x
..
.
= e for x (the exponent tower is infinite).
2. (a) The linear approximation of f (x) at 0 is the function
L(x) = a0 + a1 x,
where a0 and a1 are constants, such that
L(0) = f (0) and L0 (0) = f 0 (0).
(In other words, L(x) is the line whose value and slope agree with f (x) at 0.) Find the linear
approximation of ex at 0.
2. (b) The Maclaurin series of f (x) is the “infinite polynomial”
M (x) = a0 + a1 x + a2 x2 + a3 x3 + · · · ,
where a0 , a1 , a2 , . . . are constants, such that
M (0) = f (0), M 0 (0) = f 0 (0), M 00 (0) = f 00 (0), M 000 (0) = f 000 (0), . . . .
Find the Maclaurin series of ex .