Limits

Question 1

What does a limit describe?

Answer 1

The f(x) value that a function appoaches at its x value approaches a certain number.

Question 2

What is a left-hand limit?

Answer 2

The limit of a function as it approaches a number from the left (from negative infinity).

Question 3

What is a right-hand limit?

Answer 3

The limit of a function as it approaches a number from the right (from positive infinity).

Question 4

What criteria must exist for a limit to exist?

Answer 4

• The left-hand limit must exist
• The right-hand limit must exist
• These two limits must be equal

Question 5

lim x–> a (f(x) ± g(x)) = ?

Answer 5

lim x–>a (f(x)) ± lim x–>a (g(x))

Question 6

lim x–>a (f(x) · g(x)) = ?

Answer 6

lim x–>a (f(x)) · lim x–>a (g(x))

Question 7

lim x–>a (c · f(x)) = ?

Answer 7

c · lim x–>a (f(x))

Question 8

lim x–>a (f(x)/g(x)) = ?

Answer 8

[lim x–>a f(x)]/[lim x–>a g(x)] if lim x–>a g(x) ≠ 0

Question 9

If a function f is discontinuous on a point a, does lim x–>a f(x) exist?

Answer 9

No

Question 10

What functions are continuous everywhere in their domains?

Answer 10

Polynomials, exponential, logarithmic, sin, cos, sin^-1, cos^-1, and root functions

Question 11

For functions that are continuous everywhere, how do you find the limit at x = a?

Answer 11

Plug a in for x and solve.

Question 12

What can we say about a function at point x = a if lim x–>a f(x) = f(a)?

Answer 12

The function is continuous at a