### Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

# limits

No description
by

## Sarah Luken

on 30 August 2013

Report abuse

#### Transcript of limits

limits
DEFINITION
examples
FIND THE MAXIMUM AREA OF A RECTANGLE
in a rectangle with a perimeter of 24,

2w + 2l = 24
l = 12 - w
A = (12 - w)w
= 12w - w²

Limits That Do Not Exist
left and right
unbound
oscillating
basic limits
sally luken
ap calculus

If f(x) becomes arbitrarily close to a unique number L as x approaches c from either side, then the limit of f(x) as x approaches c is L
12 - w
W
the maximum value for A is when w = 6
"the limit of A as w approaches 6 is 36"
lim A = lim (12w - w²) = 36
w-->6 w-->6
EXAMPLES OF NONEXISTENT LIMITS
lim abs(x)/x
x-->0
lim sin (1/x)
x-->0
no matter how close x gets to 0, there will always be both +/- x-values that yeild
f(x) = {1, -1}

SO LIMIT CANNOT EXIST
no matter how close x is to 0, you could choose values of x that yeild
f(x) = {1, -1}
lim 1/x²
x-->0
because f(x) is not approaching a specific real # L as x approaches 0, you know that the limit does not exist
the existence or non-existence of f(x) at
x=c has no bearing on the existence of the
limit of f(x) as x--> c.
let b and c be real #s and n
be a positive integer:
1. lim b=b

2. lim x=c

3. lim x^n = c^n

4. lim √x = √c

x-->c
x-->c
x-->c
n
n
x-->c
estimating limits numerically
CONSIDER : lim(4x-2)

x-->2
from this information you can estimate that the limit is 6
so : f(x) = 4x-2

construct a table with
2 sets of values for x,
one from the left and
one right
the end