Derivatives
d/dx (sin x)
cos x
What is the limit of sin(x)/x as x approaches 0
1
Profit function
P(x) = R(x)-C(x)
What is the formula for the area of a triangle
area = (bh)/2
The derivative of xn where n is a constant
nxn-1
d/dx (ex)
ex
True or False: If a function is continuous at a point, it must also be differentiable at that point
False
Break Even point function
C(x) = R(x)
What is the formula for the area of a trapezoid
area = (b1 +b2)/2(h)
The formula used to find the derivative of the product of two functions, f(x) and g(x)
f'(x)g(x) + f(x)g'(x)
d/dx (ln x)
1/x
Find the limit of
(2x2-3x+1)/(x-1) as x approaches 1
-2
Function for when profit is maximized
C'(x) = R'(x)
The formula for the volume of a sphere
V = (4/3)(pi)(r3)
The derivative of the quotient f(x)/g(x), where both f(x) and g(x) are differentiable and g(x) is not 0
f'(x)g(x) - f(x)g'(x)/g(x)2
d/dx (cot x)
-csc2x
What does it mean for a function to have a discontinuity at x=a
The function is not continuous at x=a
What is the compound interest formula
A = P(1+r/n)nt
The formula for the volume of a cylinder
V = (pi)(r2)(h)
The rule used to differentiate a composite function f(g(x))
f'(g(x))g'(x)
d/dx (csc x)
-cscxcotx
What is removable discontinuity
When the limit exists but is not equal to the function's value
What is the formula for interest compounded continuously
A = Pert
The formula for the volume of a rectangular pyramid
V = (1/3)lwh
The method used to simplify the integration of composite functions by substituting u for one of the functions
u-substitution