AP Calc AB Unit 1 Review

Calculus Prerequisites

100

ln(e)

1

200

Name the real and complex solutions to f(x)=x⁴-1

x=1

x=-1

x=i

x=-i

300

1+tan²(x)=?

sec²(x) or 1/cos²(x)

400

True or false: ln(e⁵)=(ln(e))⁵.

False.

500

sin²(x) can be rewritten as this double angle identity.

(1-cos(2x))/2

ABCs of Calculus

100

When a function approaches a specific value at infinity, without actually touching that value, it is sometimes called this, also read "the limit as x approaches infinity..."

Asymptote.

200

When dealing with composite limits, you must consider what a limit does as it approaches from above and ____________.

Below.

300

When a limit involves radicals, it may require you to multiply by the ______________________.

Conjugate.

400

A Greek letter often used as a compact form for saying "the change in a variable..."

Delta

500

A Greek letter used more commonly in more rigorous definitions of calculus, typically used to represent an arbitrarily close value to 0.

Epsilon

Continuity

100

This type of function is considered to be continuous over its entire domain and has alternating infinite end behaviors.

Odd polynomial

200

A function that is said to have a removable discontinuity is also said to have this, which are usually factors that cancel out in both the numerator and denominator.

Holes

300

List the 3 conditions that must exist to show a function is continuous at any given point.

1. The function value must exist.

2. The general limit must exist.

3. The function value must equal the general limit at that point.

400

A type of discontinuity typically associated with piecewise functions where a function may be continuous literally everywhere else except for one particular x value.

Jump discontinuity or point discontinuity.

500

Create an example of a function where the general limit exists at a point but the function is not continuous at that point.

*Instructor's discretion*

Limits

100

The limit as x approaches 4 of 2x-3.

5

200

The limit as x approaches 0 from the right of ln(x).

-∞

300

The limit as x approaches 0 of sin(x)/x.

1

400

The limit as x approaches infinity of -|4x+7|/|2x-5|

-2

500

The limit as x approaches 0 of (1-cos(x))/x

0

Mathfluencers

100

One of the primary founders of calculus, famously had an apple fall on his head, and somehow didn't get a concussion.

Newton or Isaac Newton

200

Famous Greek mathematician that established a²+b²=c².

Pythagoras

300

Mathematician with the identity named after him for e^ix=cos(x)+i*sin(x), and more famously, e^iπ+1=0. 

Euler

400

A famous mathematician, originally from India, who taught himself mathematics despite having no formal or rigorous training, relying primarily on intuition, yet was well known in the pure math field; and has a movie about his works, "The Man Who Knew Infinity."

Ramanujan

500

Another lesser known founder of Calculus, often paired with Newton

Liebniz