Calculus

Fill in the blank

100

Velocity is said to be the ____________ of position.

What is the first derivative?

200

Velocity is said to be the _________________ of acceleration.

What is an antiderivative?

300

If f''(x) changes sign at x = a, then f has a(n) ______________ at x = a.

What is an inflection point?

400

A definite integral is defined as the limit of a sum of infinitely many ___________________  bounded in between a curve and the x-axis with infinitely small width.

What are rectangles.

500

In the great green room there was a telephone and a red balloon and a picture of _____________________________

What is the cow jumping over the moon.

Derivatives

100

Derivative of: csc x

What is: - csc x cot x

200

Derivative of: f(g(x))

What is: f'(g(x)) * g'(x) 

300

Derivative of: ln(3x)

What is: 3/3x

400

Derivative of: e^2x

What is: 2e^2x

500

Derivative of y with respect to x of:   2xy

What is: 2y + 2x (dy/dx)

Limits

100

If a limit of f(x) approaches different values as x approaches c, then the limit is said to be this.

What is non-existent (DNE)?

200

The derivative of f(x) is defined as a limit of this as h approaches 0.

What is (f(x+h) - f(x)) / h .

300

The value of the limit of (3x²-4x+2)/(1-x²) as x approaches positive infinity.

What is -3

400

This is the value of the limit of ln(x)/e^2x as x approaches positive infinity.

What is 0.

500

The Limit as x approaches 2 for

 (x²+x-6)/(x²-4).

What is 5/4?

Integrals

100

∫sin(x)dx

What is: -cos(x) + C

200

∫(x^-1/2)dx

What is: 2x^1/2 + C

300

∫sec²(x)dx

What is: tan(x) + C

400

∫f'(g(x))*g(x) dx

What is: f(g(x)) + C

500

∫cos(2x) dx

What is: .5sin(2x) + c

Theorems/Formulas

100

If the limit as x approaches c of f(x) from the right and left are = to f(c), the function is said to be this.

What is continuous?

200

This theorem says that if a continuous function on [a,b] has f(a) < f(c) < f(b), then c must exist on the interval [a,b].

What is the Intermediate Value Theorem.

300

The Funcamental Theorem says that the integral of 

f '(x) from a to b will equal this.

f(b) - f(a)

400

For a differentiable and continuous function on (a,b), The Mean Value Theorem says there exists at least one value of c such that this happens.

What is f'(c) = (f(b) - f(a))/ (b - a)

500

If f(x) and g(x) are inverses of each other on some interval, then this is how you find g'(c).

1/ f'(g(c))