P.o.D.
1.) Find the 19th term in the sequence for which and d= -2.
2.) Find for the arithmetic series for which and d=6.
3.) Form a sequence that has two geometric means between 56 and 189.
4.) Find the sum of the first 8 terms of the series 3-6+12-…
12-1: Introduction to Limits
Learning Target(s): I can use the definition of a limit to estimate limits; determine whether limits of functions exist; use properties of limits and direct substitution to evaluate limits.
Consider the graph of the function y=f(x) shown below:
a.)Find f(-2) and
b.)Find f(-1) and
c.)Find f(1) and
*The ______of a ______function can be found by direct ______.
Evaluate each limit.
a.)
b.)
*A function is ______if and only if ______.
The following are examples of continuous and non-continuous graphs.
Continuous / Non-continuous*Generally speaking, functions are ______if you can draw them ______lifting your ______from the ______.
EX: According to the special theory of relativity, the mass of a moving object, as measured by an observer at rest, increases as its speed increases. If is the mass of the object when it is at rest, then its mass when traveling at speed is given by the formula , where is the speed of light. What would happen to the mass of an object approaching four-fifths of the speed of light?
Evaluate each limit.
a.)
b.)
c.)
d.)
Evaluate each of the following limits on your own:
a.)
b.)
c.)
EX: Find the limit of
EX: Find the limit of .
Remember, we can always approximate a limit on the calculator.
The Rationalizing Technique:
EX: Find the limit of
EX: Approximate the limit of .
EX: Approximate the limit of
One Sided Limits:
-Sometimes a ______will fail to ______if a function approaches a ______value from the ____ side than it approaches from the _____ side.
EX: Find the limit as x0 from the left and the limit as x0 from the right for
EX: Find the limit of f(x) as x approaches 2.
The Difference Quotient:
EX: For the function given by , find
HWPg.8703-48 3rds, 60-68E, 78-88E