Derivatives and integrals
If the f(x) = cos x, then this is f'(x).
What is - sinx?
This is the differential equation that describes "the rate of change of F with respect to s is proportional to x".
What is dF/ds = kx?
This is the name for a graph that shows all the particular solutions to a differential equation.
What is a slope field?
This is the derivative of x2 + y2 = 9.
What is y' = - x/y?
For the exponential equation, y = a(b)t, this is what "a" represents.
What is the initial value?
If f(x) = ax, then this is f'(x).
What is ax ln(a)?
This is the differential equation that describes "the rate of change of R with respect to x is inversely proportional to d2".
What is dR/dx = k/d2?
If y' = 1 - xy, then this is the slope of the tangent line to the curve of y through the point (-1,-2).
What is - 1?
This is the derivative of xy = 7.
What is y' = -y/x?
This is the model we use for the derivative of y = a(b)t.
What is dy/dt = ky?
If f'(x) = x-1, then is f(x).
What is ln|x| + C?
If y' = 4x + 2, then this is the general solution for y.
What is 2x2 + 2x + C?
If y' = 1 - xy, then this is the equation of the tangent line to the curve of y through the point (-1,-2).
What is y = - x - 3?
This is the general solution for y' = x2.
What is y = x3/3 + C?
This is the model solution we use for the differential equation y'(t) = ky.
What is y = Cekt?
If f'(x) = sec2(x), then this is f(x).
What is tan(x) + C?
If f'(x) = 4x + 2 and f(-1) = 3, then this is the particular solution for f(x).
What is f(x) = 2x2 + 2x + 3?
If there are horizontal lines on a slope field, this means the slope is equal to this.
What is 0?
This is the general solution for y' = (sin x)(y2).
What is 1/(cos x + C)?
Given y'(t) = 6y and y(0) = 5, then this is the particular solution for y.
What is y = 5e6t?
If f'(x) = tan(x) cos(x), then this is f(x).
What is - cos(x) + C?
If y' = e2x -2x2, then this is the particular solution of y when y(0) = 4.
What is 0.5e2x - (2/3)x3 + 3.5?
If there are vertical lines on a slope field, this means the slope is this.
What is undefined (does not exist)?
This is the particular solution for y' = (xy)2 when y(1) = 1.
What is y = 3/(4 - x3)?
A population (y) grows based on the equation y'(t) = ky, where t is measured in years. If the population doubles every 7 years, then this is the value of k.
What is 0.099 ((ln 2)/7)?