Math 140 LA Evening Session Week 6
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Math 140
LA Evening Session Week 6
Question 1 Find the derivative for each of the following functions. Do NOT simplify.
(a) h(x) = (2x − 9)(4ex + 1)
(b) k(t) = (t − 8t−1)(et + t2)
ax + b
x2 + 3ex
(d) g(x) = 5c + 4√x
Q(x)R(x)
(e) s(x) =
P (x)
(c) f (x) =
cx + d
(f) r(x) = xR(x) + Q(x)
Question 2 Current I (measured in amperes), voltage V (measured in volts) and resistance R (measured in ohms) in a circuit are related by Ohm’s Law:
V
I = . R
dI
(a) 
Assume V is constant and calculate
dR
dV
(b) 
Assume I is constant and calculate
dR
when R = 6. State the units of your calculation.
when I = 4. State the units of your calculation.
Question 3 The total amount of crude oil Q(t) produced worldwide up to time t is is graphed below.
(a) Sketch the derivative Q′(t) for 1900 ≤ t ≤ 2150.
(b) Approximate the year for which Q′(t) is largest.
(c) Evaluate lim Q(t) and interpret. Provide units.
t→∞
(d) Evaluate lim Q′(t) and interpret. Provide units.
t→∞
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Question 4 In 1999, the population of Richmond-Petersburg, Virginia, metropolitan area, was 961,400 and was increasing at a at roughly 9200 people per year. The average annual income in the area was $30,593 per capita, and this average was increasing at about $1400 per year. Use the product rule to estimate the rate at which total personal income was rising in the area at this time. Explain the meaning of each term in the product rule.
2022-10-14