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Multiple Choice
Free Response
Free Response
Free Response
Free Response
100
6.) d/dx (x²sinx²)=
D.) 2xsin²x+x²sin2x
100
6a.) Find the limit as x approaches 0 of f(x)+1/sinx
the limit as x approaches ) is 0/0 or ind.
100
7a.) Find all values of x on the open interval 0
1 local min at x=6
100
8a.) Find the area of R
7.333 units sq.
100
Use the data in the table to approximate C'(3.5). Show the computations that lead to your answer, and indicate the units of measure.
1.6 ounces/min
200
7.) The normal line to the curve Y=(x²-1)/(x²+1) at x+2 has a slope
D.) 8/25
200
6b.) Use Eulers method, starting at x=0 with two steps of equal size, to approximate f(1/2)
-3/8
200
7b.) Determine the absolute minimum value of f on the closed interval 0≤x≤8. Justify your answer.
Min value on the closed interval [0,8] is -8
200
8b.) The region R is the base of a solid. For each y, where 0≤y≤2, the cross section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 2y. Write, but do not evaluate, an integral expression that gives the volume of the solid.
₀∫² 2x⁴+4x^3-22x²-24x+72 dx
200
9b.) Is there a time t, 2≤t≤4 at which C'(t)=2? Justify your answer.
Yes according to the MVT.
300
8.) If f and g are differentiable functions and h(x)=f(x)e^g(x), the h'(x)=
B. ) f'(x)e^g(x)+f(x)e^g'(x)
300
6c.) Find y=f(x), the particular solution to the differential equation with initial condition f(0)=-1
y=-1/x²+2x+c
300
7c.) On what open intervals contained in 0
0
300
8c.) There is a point P on the graph of f at which the line tangent to the graph of f is perpendicular to the graph of g. Find the coordinates of P.
(.25,.5)
300
9c.) Use a midpoint sum with three subintervals of equal lenght indicated by the data in the table to approximate the value of 1/6 ₀∫⁶ C(t)dt, Using correct units, explain the meaning of 1/6 ₀∫⁶ C9t)dt in the context of the problem.
10.1 ounces, is the average ounces of coffee in the cup.
400
9.) The graph of y=f(x) is show above. Which of the following could be the graph of y=f'(x)?
D.)
400
What is Dylan's Middle Name?
Bard
400
7d.) The function g is defined by g(x)=(f(x))^3. If f(3)=-5/2, find the slope of the line tangent to the graph of g at x=3
75
400
What came first the Butterfly or the Cocoon?
One of them
400
9d.) The amount of coffee in the cup, in ounces, is modeled by B(t)=16-16e^-0.4t. Using this model, find the rate at which the amount of coffee is changing when t=5.
.866 ounces/min
500
10.) e∫e² [√x+(1/√x)]²
D.) e⁴/2+3e²-2e+1
500
What game are the juniors/seniors playing at school right now?
Assassin
500
Find the area in the second quadrant enclosed by the coordinate axes and the graph of r.
47.513 units sq.
500
10b.) For ∏/2≤θ≤∏, there is a point P on the polar curve r with x-coordinate -3. Find the angle θ that corresponds to point P. Find the y-coordinate of point P. Show works that leads to your answers.
Θ=.642∏, y=6.272
500
10c.) A particle is traveling along the polar curve r so that its position at time t is (x(t),y(t)) and such that dθ/dt=2. Find dy/dt at the instant that θ=2∏/3, and interpret the meaning of your answer in the context of the problem.
-3.575 velocity in the y direction