Algebra vs. Calculus

1. 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?

Difference: when function is discontinuous

(eg.removable discontinuity at x=c)

Finding the limit of f(x) at x=c is finding the y value as the graph approaches c. Where the function may have a hole at x=c, the limit still exists. But when plugging in the number x=c, the output will ibe the exact y value of the function.

for example.

here, the limit f(x) as x approaches the point of discontinuity (lets call this c) does exist. the limit will be the y value of the open dot. but when plugged in x=c into the equation... the output will become the y value of the closed(black) dot.

Same: they are only the same when the graph of the function is continuous.

2.What are the SIMILARITIES between finding the derivative and finding the slope of a line? What are the DIFFERENCES between the two?

Similarities: find the slope and the derivative both are the change of y/ change of x. The process of finding both the slope and derivative require that you find the secant line first.

Differences: In the finding the derivative, we find the tangent line of the point by finding the secant line (picking two points close by) then bring them closer to x=c (or wherever you are finding the derivative for) this is done with limits.

so basically, finding the derivative is like finding the tangent line at that one exact point; whereas finding the slope, you pick two points .(well thats how i would put it)

Excited about monday. Its going to be funny!!

Limits

oh geez. I forgot. So im late.

hmm limits.

1. I don't get number 3 from the test: lim 6sinx/7x (as x aproaches 0).

I cant plug 0 into x directly because there's still an x in the denominator.

what if i split up the problem and change it to lim 6/7 (as x approaches 0) multiply by lim sinx/x (as x approaches 0).

since lim sinx/x (as x approaches 0) equals to 1. and lim 6/7 equals to 6/7. would my answer simply be 6/7????

2. i didnt get number 14 on the test either.

i redid th problems.. then here are the answers that i got:

a) 1

b) 0

c) 2

3. number 17 b on the test. when it said fin a right end behavior model for f.

the original equation is (x^3 - 2x^2 + 1)/(x^2+3)

so i changed it to (x^3)/(x^2) which becomes x

therefore the right end bahavior model would be just x right???

one more problem is the odd and even.. ugh. i've been getting all odd and evens wrong!!!

i eventually found out when i put the equation on the grapher. and its odd right??

i dont know how to do it without seeing the picture.