Analysis Homework #4
due Thursday, Dec. 16
1. Find the values of x for which 6x3 + x < 5x2 .
2. Compute each of the following limits:
L = lim
x→+∞
1 + 2x − x2
,
3 − 2x + x2
M = lim
x→−∞
x3 − 2x + 1
.
x4 + 2x − 3
3. Use the definition of the derivative to compute f ′ (y) when
f (x) = ax3 + bx2 + cx + d
for some constants a, b, c, d ∈ R.
4. Find the min and max values of f (x) = 3x4 − 16x3 + 18x2 over [−1, 1].
• You are going to work on these problems Friday in class.
• When writing up solutions, write legibly and coherently. Use words, not just symbols.
• Write your name and then MATHS/TP/TSM on the first page of your homework.
• Your solutions may use any of the results stated in class (but nothing else).
• NO LATE HOMEWORK WILL BE ACCEPTED.