Diagnostic Test
Applications of Diff. Calc
Misc. 1
Misc. 2
Pop Culture
100
lim (x→∞)⁡ of ((3x)^2)-4)/(2-7x-x^2) is
What is -3
100
The equation of the tangent to the curve y = x sin x at the point ((π/2), (π/2)) is
y = x
100
The maximum value of the function f(x) = (x^4) - (4(x^3)) + 6 on [1,4] is
6
100
If y = e^(-x^2), then y''(0) equals
-2
100
The 2016 summer Olympics were held in which city?
Rio, Brazil
200
If y is a differentiable function of x, then the slope of the curve of (x(y)^2)) - 2y + (4(y)^3)) = 6 at the point where y = 1 is
What is -(1/18)
200
The best approximation, in cubic inches, to the increase in volume of a sphere when the radius is increased from 3 to 3.1 in. is
3.6π cubic inches
200
A rectangle with one side on the x-axis is inscribed in the triangle formed by the lines y = x, y=0, and 2x + y = 12. The area of the largest such rectangle is
6
200
Let f(x) = cos x and g(x) = (x^2) - 1 Find the coordinates of any points of intersection of f and g
(1.177,0.384) and (-1.177,0.384)
200
Howard Wolowitz is a character from which popular U.S. TV show?
Big Bang Theory
300
Find the area of the first quadrant region bounded by y = x^2, y = cos (x), and the y-axis
0.547
300
The sum of squares of two positive numbers is 200; their minimum product is
No minimum exists
300
The volume obtained by rotating the region bounded by x = y^2 and x = 2 - y^2 about the y-axis is equal to
16π/3
300
Let f(x) = cos x and g(x) = (x^2) - 1 Find the area bounded by f and g
3.114
300
Which song topped the Billboard charts for 14 consecutive weeks in 2015?
Uptown Funk by Mark Ronson featuring Bruno Mars.
400
At noon, an experimenter has 50 grams of a radioactive isotope. At noon 9 days later only 45 grams remain. To the nearest day, how many days after the experiment started will there be only 20 grams?
78 days
400
The line y = 3x + k is tangent to the curve y = x^3 when k is equal to
2 or -2
400
A maple-syrup storage tank 16 ft high hangs on a wall. The back is in the shape of a parabola y = x^2 and all cross sections parallel to the floor are squares. If syrup is pouring in at the rate of 12 ft^3 per hour, how fast is the syrup level rising when it is 9 ft deep?
What is 1/3
400
Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed in the region bounded by the graphs of f(x) = 8 - 2x^2 and g(x) = (x^2) - 4
((4(square root of 3))/3)*8
400
Who won the 2016 Best Actor Oscar?
Leonardo di Caprio for his role in The Revenant.
500
Let y = f(x) be the function that has an x-intercept at (2,0) and satisfies the differential equation (x^2)(e^y)(dy/dx) = 4. Solve the differential equation, expressing y as a function of x and specifying the domain of the function.
y = ln (3-(4/x)) Domain is x > 4/3
500
A tangent drawn to the parabola y = 4-x^2 at the point (1,3) forms a right triangle with the coordinate axes. The area of the triangle is
25/4
500
At an outdoor concert, the crowd stands in front of the stage filling a semicirclular disk of radius 100 yd. The approximate density of the crowd x yd from the stage is given by D(x) = (20/(2 square root of x) +1) people per square yard. About how many people are at the concert?
19,500
500
Sketch the region in the first quadrant bounded above by the line y = x + 4, below by the line y = 4 - x, and to the right by the parabola y = (x^2) + 2. Then find the area of this region.
2 1/6 or 13/6
500
In the Ice Age movies, what is the name of the woolly mammoth?
Manny (short for Manfred).
M
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