Evaluating Limits

Evaluating Limits

Limits of Polynomial and Rational Fuctions

1.       If p is a polynomial function and c is a real number, then

     

     2. If r is a rational function given by                                                                and c is a real number, then





To find the limit of a polynomial or rational function, you can do a few things.

The first is direct substitution. This means that you take the number that x is approaching and substitute it in for x in F(x).

Example:

7(-3) +12

-9

The second is by dividing out. This means that you have to factor the numerator and denominator and divide out the common factors, and then use direct substitution.

Example:

(x+1)

1+1

2

The third is the rationalizing technique. This is when you first rationalize the numerator of a function.

Example:

Using direct substitution, this would be indeterminate, or
  However, you can rewrite the fraction by rationalizing the numerator.

 Now the problem can be solved by direct substitution. when 0 is put into the equation for x, the limit can be determined to be negative one half.

Arithmetic Sequences

9.2 Arithmetic Sequences

Arithmetic Sequence:
3,8,13,18,23,...

In an arithmetic sequence there is always a common difference between terms. The common difference is given the variable of d.

To find the nth term of an arithmetic sequence:

Example:





First find the common difference using the formula to find the slope of a linear equation.

Now, plug 3 in for d and the other information given and solve.

To find the sum of a finite arithmetic sequence with n terms:

Example:

Properties of Logarithms

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Change of Base Formula

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