The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111-114, a. Write the domain of f interval notation. b. Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d. Identify any other value of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e. Identify the graph of the function. f x = 2 x − 2 x 2 + 2 x − 3
The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111-114, a. Write the domain of f interval notation. b. Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d. Identify any other value of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e. Identify the graph of the function. f x = 2 x − 2 x 2 + 2 x − 3
Solution Summary: The author explains how to determine the domain of f in the interval notation for the function.
The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111-114,
a. Write the domain of f interval notation.
b. Simplify the rational expression defining the function.
c. Identify any vertical asymptotes.
d. Identify any other value of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous.
3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot
mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external
force of 4 cos 2t lb.
a. Set-up the differential equation and initial value problem for the system.
b. Write the function in phase-amplitude form.
C.
Determine the transient solution to the system. Show your work.
d. Determine the steady state of this system. Show your work.
e.
Is the system underdamped, overdamped or critically damped? Explain what this
means for the system.
4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a
capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge
60
to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the
following questions
a. Find the function that models the charge of this circuit.
b. Is the circuit underdamped, overdamped or critically damped?
1. Solve the initial value problem:
y" -11y' + 30y = x³e6x
y(0) 11, y'(0) = 36
=
Elementary Statistics: Picturing the World (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.