Derivatives
The amount by which a function is changing at one given point.
What is a derivative?
This application can be used to simplify and solve limits.
What is L'Hôpital's rule?
This is what the reverse process of taking a derivative called.
What is antidifferentiation/ integrating?
The nth-Term is used to test this.
What is divergence?
This person found a popular method of solving first order first-degree differential equations, given an initial value.
Who is Euler (Leonhard Euler)?
Find the derivative of 1/(9x3).
What is (-x-4)/3?
Find the critical points of the function g(x) = 3x4 -4x3.
What is x = 0 and x = 1?
This is the name of a common theorem used for solving definite integrals (bounded by an interval).
What is the Fundamental Theorem of Calculus?
This is the formula for finding the sum of an infinite geometric series.
What is a/(1 - r)?
This equation is used to find the x-coordinate when converting from polar-to-rectangular.
What is x = r*cos(theta)?
Find the derivative of g(x) = 6x5 - 4x3 + 3x2 - 6x + 4 at x = 2.
What is 438?
Find what direction the particle is moving in (to the left, right, or nowhere) at time, t = 5. Its displacement function is defined by x(t) = 3t2 - 28t + 24.
What is moving to the right?
g'(x) = 6x3 + 4x2 + 6. If g'(x) = is the derivative of g(x), find g(x).
What is g(x) = (3/2)x4 + (4/3)x3 + 6x + C ?
Find if the infinite series: 1/(n3/2), which starts at n=1, diverges or converges.
What is converges?
The path of a bug (in centimeters), at time t, can be found with the equation f(t) = 3t2 + 12t + 4. Find the bug's instantaneous velocity at t = 6 seconds.
What is 48 centimeters per second?
Find the derivative of (6x - 4)/(x2 + 3).
What is -6x2 + 8x + 18?
Find dy/dx for the equation: 4x2 + 2y3 + 6xy = 8, when x = 1 and y = 2.
What is -2/3?
Find the indefinite integral of: x4(3 + 4x5)1/2.
What is (1/30)(4x5 + 3)3/2 + C ?
Find the sum of the converging infinite geometric series: 16(0.50)n, which starts at n = 0.
What is 32?
This type of line has a slope of m = -1/(F'(a)) and passes through a curve at x = a.
What is a normal line?
Find the derivative of cos-1(e4x).
What is (-4e4x)/(1 - e8x)1/2 ?
If dr/dt is = 6, find dA/dt, the rate of change of the area A, when the radius is equal to 3.
What is 36pi?
Integrate xe5x dx using integration by parts.
What is (x/5)e5x - (1/25)e5x + C ?
Find if the infinite series: (6n)/(n!), which starts at n=0, converges or diverges.
What is converges?
This is the number of converging/diverging tests that can be assessed on the AP Calculus BC exam.
What is 6?