Topic 2: Limits and Forms of Indeterminate

What is a limit?

The value that the function has as a point is approached.

What is the notation of a limit?

lim x→a f(x) = L

What does L represent in a limit?

The value that the function approaches as x approaches a.

What is an indeterminate form?

An expression that is not definitively or precisely determined.

What is the difference between undefined and indeterminate?

Undefined has no value, while indeterminate has a value that cannot be precisely known.

What are examples of indeterminate forms?

0/0, ∞/∞, ∞−∞, 0(∞), 0⁰, 1∞, and ∞⁰.

What rule can be used for some indeterminate forms?

L'Hôpital's Rule.

What is the result of lim x→0 (sin x / tan x)?

1.

What is the result of lim x→0 (sin 2x / tan x)?

2.

Why is 0/0 called indeterminate?

Because direct substitution does not determine the final value.