Lecture 6: Functions and Limits

Lecture 6: Functions and Limits

Domain and Range

Example: Determine the domain and range of the function:

Determine the domain of the following functions:

c)

d)

e)

f)

INVERSE FUNCTIONS

From: http://en.wikipedia.org/wiki/Image:Inverse_Function.png

Example:

Find the inverse functions of the following function:

Example:

Example:

Example:

Example:

Solution:

Find

indeterminate form of type 0/0

Example:

Solution:

Find

2.6.1 Theorem.  If c is any number in the natural domain of the stated trigonometric function, then

EXAMPLE: Find the limit

Since the cosine function is continuous everywhere, it follows from Theorem 2.5.5 Theorem that

Thus,

Obtaining Limits by Squeezing !

Multiplying through by

taking reciprocals reverses the inequalities, so we obtain

the Squeezing Theorem implies that

?

?Since

it follows that if , then

Squeezing Theorem implies that