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1. horizontal versus oblique asymptote
a. under what circumstances does a rational function have a horizontal asymptote of y=0
b. under what circumstances does a rational function have a horizontal asymptote that is not y=0
c. under what circumstances does a rational function have an oblique asymptote
d. find horizontal and /or oblique asymptote for each of the following
i. f(x)=x^2-3x+8/x+1
ii. g(x)=4/x+1
iii. h(x)=3x+4/x+1
e. what are the vertical asymptote for each of the functions f, g, and h in problem 1d?
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A student asks if the precision with which manufacturers must calibrate their tools is at all related to statistics. How do you respond?
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If three resistors with resistance of R1, R2, R3 are wired in parralle, their combined combined resitance R is given by the following formula:
1/R= 1/R1 + 1/R2 +1/R3
The design of a voltmeter requires that the resitance R2 be 80 ohms greater than the restance of R1, that the restance of R3 be 5 ohms greater than R1, and that their combined restance be 10 ohms. Find the value of each resistance.
R1=________ohms
R2=________ohms
R3=________ohms
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3: Find the volume of the torus shown using:
a. The Shell Method.
b. The Washer Method.
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Show that if the opposite angles of a quadrilateral add up to two right angles, then the vertices are concyclic
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A tank contains 400 gallons of brine (salt in solution) in which 125 pounds of salt has been dissolved. Freshwater (with no salt added) runs into the tank at a rate of 4 gallons per minute, and the stirred mixture is drained from the tank at the same rate. (1) Find the amount of salt in the tank after an hour. (2) How long does it take to reduce the amount of salt in the tank to 10 pounds?
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Find all pairs of x and y for both of the following two equalities hold:
x + y = 10
xy - 4
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A tank contains 90 kg of salt and 2000 L of water: Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 4 L/min. What is the amount of salt in the tank initially? Find the amount f salt in the tank after 4.5 hours. Find the concentration of salt in the solution in the tank as the time approaches infinity. (Assume your tank is large enough to hold the solution.)
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In this problem, p is in dollars and x is the
number of units.
Find the producer's surplus for a product if its demand function
is
p = 144 − x2 and its supply function is p = x2 + 12x + 130.
(Round your answer to two decimal places.)
In this problem, p is in dollars and x is the
number of units.
The demand function for a certain product is
p = 123 − 2x2
and the supply function is
p = x2 + 33x + 36.
Find the producer's surplus at the equilibrium point. (Round
x and p to two decimal places. Round your answer
to the nearest cent.)
$
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Differential Calculus - [Related Rates]
—
At Noon, ship A is 200 km east of ship B and ship A is sailing north at 30 km/h. ten mins later, ship B starts to sail south at 35 km/h.
a) What is the distance between the two ships at 3pm?
b) How fast (in km/h) are the ships moving apart at 3pm?
—
Source Material:
Stewart, J. (2016). Single variable calculus: early transcendentals. [Chapter 3.9]
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Use Newton's method to find all real roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)
8/x = 1 + x^3
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Calculate k(t) when r(t) = <4t^-1,-6,6t>
Thank you!
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A manufacturing firm has a monthly production of units modeled
by?(?, ?) = 50?0.7?0.3 where x is the number of units of labor and
y is the number of units of capital.
The company has a budget of $75,000 per month for labor and
capital. If each unit of labor costs $30 and each unit of capital
costs $25, how much should the company spend on labor and materials
in order to maximize their production?
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Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x → ∞ 3x − 1 / 2x + 5
In: Math