Limits & Continuity
The value that (x^2-1)/(x-1) approaches as x approaches 1.
2
The derivative of f(x)=x^5
5x^4
The slope of the tangent line to f(x)=x^2+3x at x=2
7
The antiderivative of f(x)=4x^3
x^4+C
The equation of the horizontal asymptote of f(x)=3x^2/(x^2+1)
y=3
The value of limx→0 sin3x/x
The derivative of f(x)=ln(3x)
1/x
The x-coordinate of a critical point for f(x)=x^3−3x^2
x=0, x=2
The derivative of F(x)=∫(2,x) sin(t^2)dt
sin(x^2)
The derivative of sec(x)
secxtanx
This theorem guarantees a root of f(x)=x^3−x−1 exists on the interval [1,2]
The Intermediate Value Theorem
The derivative of f(x)=x^2cos(x )
2xcos(x)−x^2sin(x)
The type of critical point at x=0 for f(x)=x^4
Minimum
The average value of f(x)=x on [1,3]
2
The acceleration function if s(t)=t^3−6t^2+9t
a(t)=6t−12
The value of limx→0 (√(1+x)−1)/x
1/2
The slope of the tangent line to y=√x at x=9.
1/6
The absolute maximum of f(x)=−x^2+4x on [0,3]
4
The total area between f(x)=x^2−4 and the x-axis from x=0 to x=3
23/2
The value of ∫(0,π/2)sin(x)dx multiplied by ∫(0,π/2)cos(x)dx
1
For f(x)=(x^2−4)/(x−2), the value that must be assigned to f(2) to make the function continuous at x=2
4
The derivative of f(x)=ln[(x^2sin(x))/e^3x]
x^2+cot(x)−3
The rate at which the area of a circle increases when the radius is 5 cm and the radius is increasing at 2 cm/s.
20π cm²/s?
The volume of the solid whose base is the region bounded by y=x^2 and y=4, and whose cross sections perpendicular to the y-axis are squares
128/5
The volume of the solid whose base is the region bounded by y=4−x^2 and the x-axis, and whose cross sections perpendicular to the x-axis are semicircles
521π/15