Aaron Lauve
Math 131 Fall 2013, section 08, Fall 2013
Instructor: Aaron Lauve
WebAssign
Ch.1 Review (Exam)
Current Score : – / 38
Due : Monday, September 9 2013 11:55 PM CDT
1. –/2 points
HHCalc6 1.R.010.
If g(x) = (25 − x2)/(x2 + x), find the domain of g(x). (Enter your answer using interval notation.) Solve g(x) = 0. (Enter your answers as a comma­separated list.) x = 2. –/5 points
HHCalc6 1.R.012.
For f(n) = 5n2 − 4 and g(n) = n + 1, find and simplify the following.
(a) f(n) + g(n) (b) f(n)g(n) (c) The domain of f(n)/g(n). (Enter your answer using interval notation.) (d) f(g(n)) (e) g(f(n)) 3. –/1 points
HHCalc6 1.R.016.
Solve for t using logs. (Round your answer to three decimal places.)
7 · 5t = 3 · 2t
t = 4. –/3 points
HHCalc6 1.R.024.
Consider the function y = 5 + cos(3x).
(a) What is its amplitude? (b) What is its period? (c) Sketch its graph. 5. –/8 points
HHCalc6 1.R.025.
Determine the end behavior of each function as x → +
and as x → − .
(a) f(x) = x9 f(x) → as x → +
f(x) → as x → −
(b) f(x) = 2x + 7x3 − 13x4 f(x) → as x → +
f(x) → as x → −
(c) f(x) = x−4 f(x) → as x → +
f(x) → as x → −
(d) f(x) = 8x3 − 7x2 + 4
x3 − 10
f(x) → as x → +
f(x) → as x → −
6. –/1 points
HHCalc6 1.R.026.
Which function dominates as x → ?
12 · 2x or 76,000x13
12 · 2x
76,000x13 7. –/3 points
HHCalc6 1.R.049.
The demand function for a certain product, q = D(p), is linear, where p is the price per item in dollars and q is the quantity demanded. If p
increases by $2, market research shows that q drops by five items. In addition, 100 items are purchased if the price is $550.
(a) Find a formula for the following. (i) q as a linear function of p (ii) p as a linear function of q (b) Draw a graph with q on the horizontal axis.
8. –/1 points
HHCalc6 1.R.052.
When the Olympic Games were held outside Mexico City in 1968, there was much discussion about the effect the high altitude would have on
the athletes. Assuming air pressure decays exponentially by 0.4% every 100 feet, by what percentage is air pressure reduced by moving from
sea level to a city at 7540 feet? (Round your answer to one decimal place.) %
9. –/2 points
HHCalc6 1.R.054.
During April 2006, a particular country's inflation rate averaged 0.63% a day. This means that, on average, prices went up by about 0.63%
from one day to the next.
(a) By what percentage did this country's prices increase in April of 2006? (Round your answer to two decimal places.) % (b) Assuming the same rate all year, what was this country's annual inflation rate during 2006? (Round your answer to two decimal
places.) %
10.–/1 points
HHCalc6 1.R.061.
What is the doubling time of prices which are increasing by 2% a year? (Round your answer to two decimal places.) yr
11.–/1 points
HHCalc6 1.R.062.
Find the half­life of a radioactive substance that is reduced by 30% in 40 hours. (Round your answer to two decimal places.) hr
12.–/3 points
HHCalc6 1.R.066.
In an electrical outlet, the voltage, V, in volts, is given as a function of time, t, in seconds, by the formula
V = V0 sin(120πt).
(a) What does V0 represent in terms of voltage? V0 represents average voltage.
V0 represents maximum voltage. V0 represents the difference between maximum and minimum voltage.
V0 represents the time between consecutive peaks in voltage.
V0 represents how often the voltage reaches its maximum.
(b) What is the period of this function? s (c) How many oscillations are completed in 1 second? 13.–/1 points
HHCalc6 1.R.067.
In a US household, the voltage in volts in an electric outlet is given by
V = 156 sin(120πt),
where t is in seconds. However, in a European house, the voltage is given (in the same units) by
V = 339 sin(100πt).
Compare the voltages in the two regions, considering the maximum voltage and number of cycles (oscillations) per second. The US voltage has a maximum value of 120 volts and has a period of 156 seconds, so it executes 1/156 of a cycle per second. The
European voltage has a lower maximum of 100 volts, and a slightly shorter period of 339 seconds, so it oscillates at 1/339 of a cycle per
second.
The US voltage has a maximum value of 156 volts and has a period of 1/60 of a second, so it executes 60 cycles a second. The European
voltage has a higher maximum of 339 volts, and a slightly longer period of 1/50 seconds, so it oscillates at 50 cycles per second. The US voltage has a maximum value of 120 volts and has a period of 1/78 of a second, so it executes 78 cycles a second. The European
voltage has a lower maximum of 100 volts, and a shorter period of 1/169.5 seconds, so it oscillates at 169.5 cycles per second.
The US voltage has a maximum value of 156 volts and has a period of 60 seconds, so it executes 1/60 of a cycle per second. The
European voltage has a higher maximum of 339 volts, and a slightly shorter period of 50 seconds, so it oscillates at 1/50 of a cycle per
second.
The US voltage has a maximum value of 156 volts and has a period of 120π of a second, so it executes 120 cycles a second. The
European voltage has a higher maximum of 339 volts, and a slightly longer period of 100π seconds, so it oscillates at 100 cycles per
second.
14.–/4 points
HHCalc6 1.R.069.
Water is flowing down a cylindrical pipe of radius r.
(a) Write a formula for the volume, V, of water that emerges from the end of the pipe in one second if the water is flowing at the
following rates.
(i) 3 cm/sec (ii) k cm/sec (b) Graph your answer to part (a)(ii) as a function of the following.
(i) r, assuming k is constant (ii) k, assuming r is constant 15.–/1 points
HHCalc6 1.R.077.
If possible, choose k so that the following function is continuous on any interval. (If not possible, enter IMPOSSIBLE.) f(x) = 6x3 − 12x2
x ≠ 2
x − 2
k
x = 2
k = 16.–/1 points
HHCalc6 1.R.078.
Find k so that the following function is continuous on any interval. (If not possible, enter IMPOSSIBLE.) j(x) = k = k cos x x ≤ 0
ex − k x > 0