Math Humor

Since no one seems to want to work problems unless they DON'T include sign diagrams (:-P), I thought I'd post some humor:



Cheers,

FLB

P.S. You didn't think I'd REALLY miss giving you one of these, right? :D



Okay the first thing you do for functions like this is what I call "Plug N Play." F(x) is simply your template for what you're gonna do with the values you're asked to solve for. This means in the 1/x^2, you're going to be filling in the blank for x. So when you solve for f(x+h)-f(x)/h, you're plugging in (x+h) for x, and then filling in x for x, and dividing the whole thing by h.

The result is what I show in line 1:



For line two, because we are subtracting two fractions, we have to get a common denominator. This is done by taking the first fraction times x^2/x^2 and the second fraction by (x+h)^2/(x+h)^2.

For line 3, when we simplify, we have to keep the foiled product in parentheses because we have a negative to distribute. Failure to do this will throw your whole problem off.

For line 4, we distribute the negative and see that this will eliminate our x^2's, as shown in line 5.



Line 6 we remember that anything divided by something is the same as multiplying by 1/the number, so we multiply our denominator by h. This, coupled with factoring out h in the numerator, allows us to cancel out the h and be left with our answer, which can be shown in factored form or foiled form.

CONGRATS! You made it! :) These problems are not really difficult per se, just time consuming and tedious. It is important to be very exact in your workings as a mistake in any part of the problem can render your answer incorrect.

Happy Math Hunting!

FLB