LIMITS

AP EXAM REVIEW

LIMITS

DERIVATIVES

APP DERIVATIVES

INTEGRALS

APP INTEGRALS

DIFF. EQUATIONS

- Case 1 Point: When approaching a point defined or not (Closed or Open) the limit is the y coordinate of the point you are approaching.
- Case 2 Vertical Asymptote: When approaching a vertical asymptote, the limit is infinity if you are heading up and negative infinity if you are heading downwards.
- Case 3 Oscillation: When a function oscillates toward a boundary
*x*value the limit in that case does not exist.

INTERACTIVE PRACTICE TEST

FORMULA SHEET & FLAHS CARDS

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1.Establish the fact that the limit is finite. (i.e The value that x and the f(x) approaches must not be ±∞)

2.Substitute the value x is approaching and evaluate. If 0 is in the denominator go to 3.

3.Factor, or rationalize the numerator or denominator and cancel out any removable discontinuities and substitute again. If 0 at the bottom use a non algebraic approach since the limit might not exist.

Point: Find the y coordinate of the point that you are approaching from that direction.

Horizontal Asymptote: Find the y coordinate of the equation of the line

Vertical Asymptote: One sided +/- infinity, Double sided does note exist.

The limit of a function is the value the function approaches as the independent variable approaches a value, negative or positive infinity.

“Read as the limit of f(x) as x approaches a is L”

“Read as the limit of f(x) as x approaches a is L”

Right/Left Hand Limit: The right/left hand limit of a function f(x) as x approaches a equals L is written as:

- Lines and Graphs
- Graphs and Piece-wise Defined Functions
- Domain Range Odd and Even Functions
^{Transformation of Functions Domain Range and Composition}

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- Finite Limits Algebraic and Graphical (2.1a)
- Finite Limits Squeeze Theorem (Pinch (2.1b)
- Finite Limits Graphical and Numerically one and Double sided limits (2.1 c)
- Limits Piece Wise Defined Functions (2.1d)
- Limits Involving Infinity part I (2.2a)