CM12006 Limits

What is ε? [1]

The distance |f(x) - L|

What is δ? [1]

The distance |x - c|

How is ‘the limit of f(x) as x approaches c is L’ written? [1]

What is the ε - δ definition of a limit? [3]

If for every number ε > 0, there is a number δ > 0 such that

If 0 < |x - c| < δ

Then |f(x) - L| < ε

What are the 2 steps for solving an ε - δ definition problem? [2]

Guess a value for δ

Showing that this δ value works

How do you guess a value for δ? [2]

Rearrange |f(x) - L| into the form |x - c|

How do you show that this δ value works? [2]

Sub back into equation

What is the sum law? [1]

What is the difference law? [1]

What is the constant multiple law? [1]

What is the product law? [1]

What is the quotient law? [1]

What is the power law? [1]

What is the root law? [1]

How do you write a left-hand limit? [1]

What is the definition of a left-hand limit? [3]

If for every number ε > 0 there is a number δ > 0

Such that c - δ < x < c then

|f(x) - L| < ε

How do you write a right-hand limit? [1]

What is the definition of a right-hand limit? [3]

If for every number ε > 0 there is a number δ > 0

Such that c < x < c + δ then

|f(x) - L| < ε

What is the relationship between limits and one-sided limits? [2]

How do you write an ∞ limit? [1]

What is the definition of an ∞ limit? [3]

For every positive number M there is a positive number δ > 0 such that

If 0 < |x - c| < δ then f(x) > M

How do you write an -∞ limit? [1]

What is the definition of an -∞ limit? [3]

For every negative number N there is a positive number δ > 0 such that

If 0 < |x - c| < δ then f(x) < N