Calculus Final Project

Derivatives

100

d/dx (sin x)

cos x

200

d/dx (e^x)

e^x

300

d/dx (ln x)

1/x

400

d/dx (cot x)

-csc²x

500

d/dx (csc x)

-cscxcotx

Limits and Continuity

100

What is the limit of sin(x)/x as x approaches 0

1

200

True or False: If a function is continuous at a point, it must also be differentiable at that point

False

300

Find the limit of 

(2x²-3x+1)/(x-1) as x approaches 1

-2

400

What does it mean for a function to have a discontinuity at x=a

The function is not continuous at x=a

500

What is removable discontinuity

When the limit exists but is not equal to the function's value

Economic Application

100

Profit function

P(x) = R(x)-C(x)

200

Break Even point function

C(x) = R(x)

300

Function for when profit is maximized

C'(x) = R'(x) 

400

What is the compound interest formula

A = P(1+r/n)^nt

500

What is the formula for interest compounded continuously

A = Pe^rt

Related Rates Formulas

100

What is the formula for the area of a triangle

area = (bh)/2

200

What is the formula for the area of a trapezoid

area = (b1 +b2)/2(h)

300

The formula for the volume of a sphere

V = (4/3)(pi)(r³)

400

The formula for the volume of a cylinder

V = (pi)(r²)(h)

500

The formula for the volume of a rectangular pyramid

V = (1/3)lwh

Deriv./Int. Formulas

100

The derivative of xⁿ where n is a constant

nx^n-1

200

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)

300

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

400

The rule used to differentiate a composite function f(g(x))

f'(g(x))g'(x)

500

The method used to simplify the integration of composite functions by substituting u for one of the functions

u-substitution