Question

Simplify the following difference quotients

Answer 1

\[\frac{ (5+h)^{2} - 125 }{ h }\]

Answer 2

expand the \[(5 + h)^2\] to get \[h^2 + 10h + 25\] simplify the numerator\[h^2 +10h + 25 -125 = h^2 +10h -100\] so, your new expression looks like this \[(h^2 + 10h -100)/h\] divide each term by h to get the following: \[h + 10 - (1/h)100\]

Answer 3

The answer in the text is \[75 + 15h + h ^{2}\]

Answer 4

is this calculus or math analysis?

Answer 5

calculus!

Answer 6

do you have a sample from the book...my understanding of difference equations deals with circuits. i may not be able to assist you.

Answer 7

I'm sorry, i dont think it gave me any exact samples like the question but they used terms such as slope of tangent, limits of slopes and there was an equation \[\frac{ f(a+h) - f(a) }{ h }\] in the summary

Answer 8

do you have the original function?

Answer 9

for instance, if \[f(x) = x^2 \] then f(x+ h) is \[ = (x+h)^2 = x^2 + 2xh + h^2\] then we would subtract f(x) and divide the whole thing by h to get \[(f(x+h) -f(x))/h) = (x^2 + 2 xh + h^2)/h\]

Answer 10

the answer would 2x as h approaches zero.

Answer 11

There is no original function for the question i asked :P sorry, im taking an independent course for calculus s my understanding is a bit vague and im having trouble understanding the content of the course

Answer 12

It's alright, i was planning on asking a teacher when I go to school

Answer 13

no worries....i think it's best.