Blog #3

1. The limit of a function is the behavior before and after a specific point.

2. You evaluate limits by plugging in the number or value that you are testing into the given function. Certain values do not always work and you will end up with an undefined equation. (Divide by zero).When this happens the equation must be rationalized. We dealt with square root functions, absolute value functions, quadratic functions, cubic functions, and lines.

Examples of functions that don't immediately work: 


Square Root Function: Evaluate the limit as x approaches 0 from the equation
The first step is to rationalize the equation by multiplying by the square root of h + 16, +4. Multiply both the numerator and the denominator. The numerator should end up being h and the denominator should end up being h times the square root of h+16, + 4. The next step would be to divide by h, leaving you with 1 over the square root of h+16, +4. Then plug in the desired value (0). The answer should be 1/8. 



Absolute Value Function: Evaluate the limit as X approaches -1 from the equation:
The first step is to plug the value (-1) in for x without the absolute value sign and solve. This answer should be one. The second step is to make what is inside the absolute value equation opposite and solve. It should be -X-1 over X+1. The answer for this is -1. Because the two answers are different, the limit does not exist for this problem.

Quadratic Function: Evaluate the limit as x approaches 5 from the equation
The first step is to factor the numerator of the equation. In this case, the factors are (X-1) and (X-5). Because there is (X-5) on the numerator and denominator, they can be cancelled. The final equation should be X-1 over 1. The final step is to plug in the desired value (5) and solve. The answer should be 4.

Cubic Function: Evaluate the limit as x approaches 0 from the equation
First, triple foil the numerator of the equation. Once the numerator is triple foiled, every number in the numerator should have an h that can be divided out. Divide by h. After this, plug your value (0) into the equation. The answer should be 12.

3. https://www.desmos.com/calculator/vyl6gaur84
 Limits do not exist at -4, -2 and 2 because the behavior on both sides of these points is not the same.
:'( <Sad Face. I'm a failure.

4. This function has an infinite limit at zero because because we can get "arbitrarily large for sufficiently close." Meaning that it goes on forever and as we get closer to zero, the y-value gets significantly larger.