Limit

What symbol is used to represent the concept of a limit in mathematics?

• lim

• Σ

• Δ

• ∫

Which of the following statements is TRUE about function limits?

• A limit can only be calculated if the function is defined at that point

• The limit of a function at a point is always equal to the value of the function at that point

• The limit depends only on the value of the function at the point

• A limit describes the behavior of a function as it gets close to a certain point

What is the definition of a limit of a function at a point a?

• The function’s value at a

• The behavior of the function as x moves away from a

• The value that f(x) approaches as x approaches a

• The maximum value of the function near a

Why might a function not have a limit at a certain point?

• The graph is not continuous

• The left-hand and right-hand limits are not equal

• The function is not defined at the point

• All of the above

• Because x =3 in the function

• Because we can simplify the expression and then put x =3

• Because the function is nice and smooth at x=3

• Because the top of the fraction becomes 0 when x=3

Based on the graph, does the function graph have a value when x is approached by 4?