Limits
The asymptote of lim x -> -∞ ex - 5
What is -5
The names of the derivatives of position in order, after acceleration
What is jerk, snap, crackle, pop
The antiderivative of
1
f(x) = ------------
1 + x2
Does the IVT apply to the function f(x) = x2 - x + 1 on [-1, 5] where f(c) = 8
Yes as f(c) falls between f(-1) and f(5)
The asymptote of
5x^3 +3x + 7
lim x -> ∞ ----------------
2x^2 + 5x - 2
What is ∞
The formula for d/dx (csc-1(u))
-u'
What is --------------
|u|√(u2-1)
The antiderivative of ∫(2x+3)3 dx
What is (1/8)(2x+3)4 + C
The x-value where the instantaneous rate of change equals the average rate of change on the interval [2, 6] for the function f(x) = -x2 + 3x + 10
What is x = 4
Suppose lim x->2 f(x) = 4, lim x->2 g(x) = 5, lim x->2 h(x) = 8. The asymptote of lim x->2 [6f(x)g(x) + h(x)]
What is 128
x3 - 3x2 +4
The value as lim x -> 2 ----------------------------
x4 - 4x3 + 7x2 - 12x + 12
6 3
What is --- ---
14, 7
The area between the curves f(x) = 5 - x2 and g(x) = x2 - 3
What is 64/3
The general solution for the differential equation
dy x2
--- = ---
dx y
y = ∓√((2/3)x3 + c)
Using conjugates, the approaching value at lim x-> 1 (√x -1)/(x-1)
What is 1/2
The X value for the absolute minimum of the function f(x) = x2ln(x) on the domain (0, ∞)
What is x = e-1/2
The volume of a solid bounded by y = x2 and y = 2 - x2 using semi-circles perpendicular to the x-axis
What is 8π/15 ≈ 1.6755
The total distance traveled by a jogger on the interval [0, 3] whose velocity is given by v(t) = 2t2 - 8t + 6 miles/hour
What is 16/3 ≈ 5.333
5(x2-4)
f(x) = ----------
x2+2x-8
lim x -> ∞ f(x) and all the horizontal asymptotes of f
what is lim x -> ∞ f(x) = 5 and y = 5
Two small planes approach an airport, one flying due west at 120 mi/hr and the other flying due north at 150 mi/hr. Assuming flying at constant elevation, how fast is the distance between the planes changing when the westbound plane is 180 miles from the airport and the northbound plane is 225 miles from the airport?
What is dc/dt = -192/hr
Let R be the region bounded by the curve f(x) = (x+1)2, the x-axis, the lines x = 0 and x= 2. The volume of the disk created by revolving R around the x-axis
What is 242π/5 ≈ 152.0530
The function that gives the total amount of cells in a culture in a lab when the growth rate is modeled by N'(t) = 90e-0.1t cells/hr and and N(0) = 100
What is N(t) = N(0) + ∫90e-0.1x dx [0, t]