Practice Final Exam - Loyola University Chicago

1. (15 points) Find the arc length function for the curve y = x3 + 3 x2 + x + 1
What is the length of the curve from (0, 1/4) to (1, 59/24) ?
4x+4 .
2. (15 points) Let P (x) = a n x n +a n−1 x n−1 +· · · a 1 x+a 0 be any polynomial function
with a i ∈ R (i = 1, · · · , n), and let E(x) = e x . Show that P = o(E) as x → ∞.
2