Question: Which of the following statements best defines the term “extraneous solution”?
Answer Choices:
A. An extraneous solution is a solution to a linear equation that contains fractions.
B. An extraneous solution is an irrational solution to an algebraic equation.
C. An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.
D. An extraneous solution is an approximate solution to an algebraic equation.
Answer: C. An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.
Question: Mixture problems can be expressed as “in-out” differential equations of the form dA/dt = r₁C₁ − r₂C₂.
Answer Choices:
T
F
Answer: T
Question: The equation r = 2cos(θ) in polar form is equivalent to which equation in rectangular form?
Answer Choices:
x² + y² = 2y
x² + y² = 4y
x² + y² = 2x
x² + y² = 4x
Answer: x² + y² = 2x
Question: dy/dx = x²y + sin(x) is in standard form.
Answer Choices:
T
F
Answer: T
Question: In a rational expression, which of the following is true about restricted values?
Answer Choices:
A. There can be more than one restricted value.
B. A restricted value is any value which causes the numerator to equal zero.
C. Zero is always a restricted value.
D. A restricted value is any value which causes the denominator to equal zero.
Answer: A and D
Question: Convert (3, –3) to polar coordinates with r ≥ 0 and θ between 0° and 360°.
Answer Choices:
(18, 225°)
(18, 315°)
(√18, 225°)
(√18, 315°)
Answer: (√18, 315°)
Question: An integrating factor for the differential equation dy/dx + p(x)y = q(x) is μ(x) = e^(∫q(x)dx).
Answer Choices:
T
F
Answer: F
Question: Which of the following statements is true about rational equations?
Answer Choices:
A. A rational equation can never lead to a linear equation.
B. When solving a rational equation, it is never a good idea to multiply both sides of the equation by the least common denominator.
C. Rational equations always have no solution.
D. It is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions.
Answer: D. It is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions.
Question: The equation x + y = 6 in rectangular form is equivalent to which equation in polar form?
Answer Choices:
r(cosθ + sinθ) = 6
r(cosθ – sinθ) = 6
r²(cosθ + sinθ) = 6
r²(cosθ – sinθ) = 6
Answer: r(cosθ + sinθ) = 6
Question: The current in an RL circuit system is of the form L dI/dt + RI = E(t), where L is the inductance, R is the resistance, I is the current, and E(t) is the electromotive force.
Answer Choices:
T
F
Answer: T
Question: There is only one possible integration factor for any given first-order linear differential equation.
Answer Choices:
T
F
Answer: F