MCQ
Let c(x)=-2x^3+3x^2+36x The absolute maximum value of g over the closed interval [-3,5] occurs at what x-value
a. -3
b. -2
c. 3
d. 5
c. 3
Approximate the area between the x-axis and s(x) = x^2 from x = 1 to x = 4 using a trapezoidal sum with 3 equal subdivisions.The approximate area is
a. 22.9
b. 55.5
c. 21.5
d. 39.8
c.
A known __________ of A(x) can be used to find a volume of a solid. Fill in the blank.
cross section
his equation's derivative is: 25x^3 - 12x^2 + X. Find its integral
25x^4/4 - 4x^3 + x^2/2 + C
The property value of Zhilinsky grows at a rate of s(t) people per year (where t is time in years).
What does ∫2-4 s(t)dt represent?
Answer: The change in number of people between the second and the fifth year.
Let s(x)=x^4-2x^3. For what value of x does s have a relative minimum.
A. 3/2
B. 0
C. 2
D. -2/3
A. 3/2
∫p^2dp= ()+C
a. 2y^2
b. y
c. 1/3y^3
d. 3y^3
c.
Find the area enclosed by y=x^2 and the y-axis between [0,3] is revolved around the y-axis
9/2 pi
State the formula of the Power Rule for Derivatives
A'b + B'a
Let P be the region enclosed by the line x=-4, the line y=1, the line y=4, and the curve y=e^x. A solid is generated by rotating P about the line x=-4. What is the name of the method that needs to be applied to solve this question?
Answer: Disk method.
Let p(x)=-2x^6+15x^5. For what values of x does the graph of p have a point of inflection?
Choose all answers that apply
a. 0
b. 5
c. 15/2
d. There is no point of inflection
a & b
Solve the equation: dy/dx=-1/3x^3
a. y=-x^(2+C)
b. y=-x^2+C
c. y=-x^4/(12+C)
d. y= -x^4/12+C
Answer: y= -x^4/12+C
Name the 4 types of Discountinuties
hole, jump, infinity, oscillating
A function fails to be differentiable if it has a... (name all four options)
discontinuity, corner, cusp or a vertical tangent
Zimmer is evaluating the expansion of his vast property holdings over time. The rate at which his property grows is given by the function v(t) = 2t + 5 (in units per year), where t represents time in years. At t = 1, his total property was already 5 units. To determine the total growth of his holdings between t = 1 and t = 3 years, should Zimmer use integration or differentiation?
Answer: Integration
A function that models the slope of the curve for all x-values for which it exists. This is the definition of what?
a. a function
b. a derivative
c. the behavior of a function
d. discontinuity
b
c’(x)=-5x^4+9x^2 and c(3)=-80
f(-3)=
a. -162
b. 82
c. 244
d. -80
Answer: 244
Name all 5 of the rules to find limits
Difference Rule, Constant Multiple Rule, Product Rule, Power Rule, Quotient Rule
Integrate the following equation ∫√(7x+9)dx
(2/21)(7x+9)^(3/2)+C
Payewski is analyzing the rotation of a wind turbine blade. The blade's angular position is described by the function theta(t) = t^4 - t^2 + 3t (in radians), where t represents time in minutes. To determine how quickly the blade's rotation speed changes at exactly t = 2 minutes, should Payewski apply integration or differentiation to the angular position function?
Differentiation
Cedric was asked to find ∫sin^5(x)cos(x)dx using u-substitution. How should Cedric define u?
a. u=sin(x)
b. u=x^5
c. u=cos(x)
d.u=sin^5(x)
e. Cedric should stop defining me using math equations
a.
A rumor comes out in the monopoly newspaper. The number of trillionaires who have not heard about the rumor decreases at a rate that is proportional at any time to the number of trillionaires who have not heard the rumor at that time. There were 900 trillionaires who had not heard the rumor initially, and the number of trillionaire is divided by 3 every 4 days.
How many trillionaires have not heard the rumor after 7 days?
Round to the nearest trilionaire.
a. 131.61
b. 132
c. 900.03
d. 900
Answer: 132
The value of a Monopoly property increases at a rate proportional to its current value at any time. The property is worth $1600 initially, and its value grows to $1920 after one year (365 days).
What is the property's value after 90 days?
Answer: $1673.57
A particle moves along a horizontal line. Its position function is s(t) for t >= 0. Find the velocity function v(t).
s(t) = t^3 - 14t^2
v(t) = 3t^2 - 28t
Zimmer is studying the production rate of his startup's new smartwatch. The rate of production is given by the function: C(t)=50t^2+200t where t is time in days since launch. If Zimmer computes the integral with lower limit 0 and upper limit 50 what real-world quantity does this represent for his business?
The integral represents the total number of smartwatches produced in the first 50 days after launch.