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.