Calculus vs. Algebra; Algebra vs. Calculus

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# What is the DIFFERENCE between finding the limit of a function at x = c and actually plugging in the number x = c? When are the two cases the SAME?

finding the limit of a function at x=c is when f(x), y, gets closer as it gets closer to c. So your finding the value of y as it approaches. Never will there be an exact point because sometimes there can be a hole at that point.
Plugging in relates to the exact point. The exact point for the value of y even if it does not really approach.
With a continuity, both are the same. with the limit of f(x) as x> c =(c) then these cases are the same. Y values are the same with the same points

# What are the SIMILARITIES between finding the derivative and finding the slope of a line? What are the DIFFERENCES between the two?
the change of y over the change of x. The formulas to finding them differ but are the same concepts.
The difference for finding a derivative is that we use limits. We use the limit as H approaches zero. We use h as the difference point, as h+ or h- The derivative is used to find the slope of a tangent line.
Finding the slope of a line is only finding the slope of that line. Finding the slope of a line at a curve is finding the tangent line..