Derivatives
The derivative of y = 4x2 + 6x + 1
What is dy/dt = 8x + 6?
∫4 dx
What is 4x + C?
Use the Trapezoidal Rule with n = 6 to approximate ∫sin2x dx from [0, π]
What is π/2?
limx→−2 (x2 + 4x +3)
What is -1?
If a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then if f(a) = f(b), there exists a point c in the interval (a, b) such that f'(c) is equal to the function's average rate of change over [a, b].
What is Rolle's Theorem?
The first derivative of 12x2 + 3x +21
What is f'(x) = 24x +3?
∫3x4 + 5x2 + 7 dx
What is 3/5x5 + 5/3x3 + 7x + C?
The equation of the tangent line to g(x) at x = −3 if f(2) = −3, f '(2) = 34, and g(x) = f -1(x)
What is y − 2 = 4/3(x + 3)?
limx→0 (2x2 + 5x +10)
What is 10?
If f(x) is continuous on the closed interval [a, b] and differentiable on (a, b) then there is at least one c between a and b where f'(c)=(f(b)-f(a))/(b-a)
What is the Mean Value Theorem?
The derivative of logx2
What is 2/lnx10?
∫sqrt(4x) dx
What is 1/6 (4x)3/2 + C?
The point on the graph of the function f(x) = x2 that is closest to the given point (2, 12).
What is (1, 1)?
limx→3 (-2x3 + 5x2 - 4x + 5)
What is -16?
Change in position/Length in time = [s(t) - s(to)/t - to ] where s(t) is the position of the particle at time t.
What is the Average Velocity?
The second derivative of 8x3 + 6x2 + 9x + 2
What is f''(x) = 48x + 12?
∫7ex dx
What is 7ex + C?
Find dy/dx if 3xy = 4x + y2
What is (3y − 4)/(2y − 3x)?
f(x) = 8/(x-4)2
limx→4- f(x)
What is +∞?
1/2(f(to) + f(t1))Δt + 1/2(f(t1) + f(t2))Δt +... + 1/2(f(tn-1) + f(tn))Δt
What is the Trapezoidal Rule?
The first derivative of 3x2(x2 +1)
What is f'(x) = 12x3 + 6x?
∫2x2 - sqrt(6)x + 2 dx
What is 2/3x3 - sqrt((6)/2)x2 +2x + C?
The acceleration at π/4 = 1 when the position of a particle is given by s(t) = sin(2t) + π/4
What is -4?
limx→4- (-5 - x3/x2 - 9)
What is +∞?
If limx→a f(x)/g(x) = 0/0 or ∞/∞ and if limx→a f'(x)/g'(x) exists then limx→a f(x)/g(x) = limx→a f'(x)/g'(x)
What is L'Hôpital's Rule?