algerbra vs. calculus

1. Well the difference between finding the limmit of a function at x=c and plugging in the number x=c is really nothing if you are finding the limit of a continuous function becasuse you will either way get the same answer, but when the function is discontinous it REALLY MATTERS.
When its a discontinous function you dont plug in the number x=c because when the function is discontinuous at a certain point, or otherwise has a jump, an empty hole(removeable discontinuity), or infinite discontinuity, you wont just be able to plug in (c) because you will get an exact output, and if the function is discontinuous there will be no exact output, thats why you find the limit of x=c becasue that will give you a y value as x=c.

2. Finding the slope and the derivative is basically the same thing because they both give you the rat at which the graph is moving. They are different because slopes are mostly used for lines and derivatives are used for for complicated functions, one example is x^3. A tangent line and a secant line is required to find the derevative of a function, thats why you can not find the derivative of a line. A tangent line is a line at the function at one point, and a secant line is a line on the graph at 2 points.

CAUTION:

THE EXPLANATION AT THE TOP MAY BE A LITTLE CONFUSING, THE WRITER IS NOT RESPONSIBLE FOR ANY HEAD ACES, OR NAUTIOUS SYMPTOMS.

lol j/k :D