MATH 110, Assignment 4
Make sure you justify all your work and include complete arguments and explanations. Please include your name and student number on the top of the first
page of your assignment.
Problem 1. Differentiate.
(a) f (u) = u sin u1
(b) y = ln(1 + ln(1 + ln x))
(c) s(t) = 3t cos t
Problem 2. Let h(x) = e2f (x) +
p
f (x) where f (1) = 4 and f 0 (1) = 2. Find h0 (1).
Problem 3. Let y(x) = erx . For what value of r does y(x) satisfies y 0 (x) + 3y(x) = 0.
Problem 4. (Multiple choice problem) If the base b of a triagle is increasing at a rate of 3
centimetres per second while its height h is decreasing at a rate of 3 centimetres per second,
which of the following must be true about the area A of the triangle? Justify your answer.
(a) A is always increasing.
(b) A is always decreasing.
(c) A is decreasing only when b < h.
(d) A is decreasing only when b > h.
(e) A remains constant.
Problem 5. The position of particle is given by the equation:
(
t ln(tt ) t > 0
s(t) =
0
t=0
where t is measured in seconds and s is in metres.
(a) Find the velocity at time t. Including units.
(b) When is the particle moving backward (that is, in the negative direction.)
(c) Draw a diagram to represent the motion of the particle.
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