Algebra vs. Calculus

1.The difference between finding the limit of a function as x=c and actually plugging in the number x=c, is that the limit of a function as x approaches c could not be a value of the function if the function is not continuous at c. In a limit you are finding the value as x is approaching the constant c which can be different to what the actual value is. When plugging in x=c to the function you are finding the exact value of the function. The best way to see the difference is through a function that is not continuous for example a piecewise function which can have several different functions with different limits when x=c or a different value when x=c.
The two cases are the same when the function is continuous were the limit when x approaches c is the same as the value of the function when x=c.

2. The similarities when finding the derivative of a line and the slope is that the value is the same in the case of a line because in both functions you are finding the change in y over the change in x. In a derivative when finding the value we use limit as h approaches 0 f(a+h)-f(a)/h meaning that we are assuming that the difference as h approaches a is infinitely small.
Derivatives are mainly used to find the slope of a point in a curve by finding the slope of its tangent line.

Limits

The whole concept of how limits worked took me a while to figure out mainly the part of discontinuity and continuity. I have trouble in trying to figure out whether a piecewise function is continuous or discontinuous.

One of the biggest problems I have is trying to figure out End behavior models for trigonometric functions without using a calculator for example problem number 38 on pg 95 which is f(x)=ln[abs(x)]+sinx. I was able to figure out the right end behavior model knowing that sinx was not really significant because the smallest value is -1 and that the biggest value is 1 so I knew that ln[abs(x)] was the right end behavior model.

I still have trouble in trying to figure out how to solve for horizontal asymptotes for a function. I am not sure whether there is a way to solve for it without having to graph it.

I was really confident about the limits test after seeing the practice test we got primarily because I did not see anything that gave me too much problem. After taking the test I was blindsided by a couple of problems on the test which is still bugging me that I was not able to solve which was one about explaining why a trigonometric function was continuous and to graph a sketch. The other one was the free response which had a piecewise function with a function having a variable on it.