Lindsey's Reflection

This week in class we discussed the continuity of different fucnctions.

For each different case there was a set of rules to follow.

These are the rules:

When you have a fraction you first have to factor the top and the bottom of the factor.
if it is possible then you must cancel with what you got from factoring.

After this you set what you have cancelled to zero and the you solve for x.

in this case you would have a removable in the problem.

if you are unable to factor and cancel anything from the fraction you have
you then set the denominator of the fraction equal to zero and from
there you solve for x.
you will get a number and whatever number you get with be the answer. In this
case you will have a vertical asymptote or an infinite in the problem.

Here is an example from classwork

limit x-5/x^2-25
x-->5+

from here you could factor and this is what you would get

x-5/(x+5)(x-5)

the x-5 can cancel from the problem.
after this you are left with x+5
now you can plug the 5 into the problem with out getting a zero
at the bottom of the fraction.

so you plug the 5 in

5+5=10

the answer of the problem is ten.

because you could cancel you have a removable.
and it is continous at (negative infinity, 10) u (10, positive infinity)


another type you may come across is a piecewise

with a piecewise you have to plug in the x values to see if they are equal.
if they are not equal it is a jump.

if the two are equal but there is no equal under the less or greater sign it is a removable.

a piecewise is a little more difficult to deal with but if you follow the
steps given it should not be too hard.