Evaluating Limits

So today we started limits. We use limits as "mathematical microscopes" to describe y-values near a given x-value. We evaluate the limits of given functions by (for now) using the calculator: Enter the function in Y1 and use the table feature to enter certain x-values. Use the y-values to determine the limit of the function. Remember to use radians when evaluating limits that involve trig. Also, keep in mind that some limits do not exist or may be deemed "indeterminate." See notes for further details.

Binomial Theorem

Today we learned about the binomial theorem. We learned the real formula on how to expand (x+y)^n. We learned the combination function and reviewed Pascal's Triangle, as both can be used to expand (x+y)^n. You can use Pascal's Triangle to find the coefficients of term. 

Proof by Induction

Sum Equations

Today in class we learned equations to find the sums of certain types of sequences.

Geometric Sequences

Monday in class we talked about geometric sequences, where there is a constant ratio between terms. We learned the equation and worked some practice problems, as usual. We also discussed finding the sum of terms in a geometric sequences, which usually has to be done on a calculator.

Arithmetic Sequence

new formula for linear functions, new term Arithmetic Sequence 

d is the constant difference between the terms 

can find the formula from a sequence, can also find a sequence from a formula 

lots of examples 

Sequences, Recursion, Sigma

Today we practiced sequences, recursive notation, and played with summation/sigma. The new things were mainly the latter 2. Recursive notation is a way of writing a sequence in such a way that the method calls itself. Recursive notation requires 2 things: An defined by a change in An-1 and a start point, a value for A1. Sigma notation is used when talking about adding everything up in a sequence. You put the lower limit on the bottom and the upper limit on the top. Next to the sigma, write the function that you will call each time to produce the next number in the sequence and that number will get added to the previous number until the upper liimit has been reached. You can use the calculator if the numbers get messy. 2nd -> Stat -> math for sum and -> ops for seq and then type in the function, variable being used, start value, end value