need help

Math 251 Written Homework 4 - Fall 2017 Due Week 5 Page 1 of 1

Name:

Instructions: Show all of your work. Put your solutions on a separate piece(s) of pa- per (8.5x11 or A4). Use this page as a cover sheet. Staple all of the pages together. Late homework is not accepted.

(1) Find the derivative of the following function. Show all of your work.

M(t) = [3te4t + t2][sin(t) + tan(t)]

e−2t + t2 − cos(t)

(2) Let g(θ) = sin(θ) + cos(θ). Find all of the θ-value(s) in the interval [0,2π] such that g′(θ) = 0.

(3) Evaluate the following limit. (You will need to use one of the special limits from section 3.5.) (Hint: factor the denominator.)

lim x→−3

sin(x + 3)

x2 + 8x + 15

(4) Let s(t) = 1

12 t4 − 10t3 be the position of an object at time t for 0 ≤ t ≤ 120.

(a) Find the velocity of the object at time t.

(b) For what value(s) of t is the velocity positive? Use interval notation for your answer.

(c) Find the t-values such that the velocity is equal to zero.

(d) Find the acceleration of the object at time t.