anonymous
  • anonymous
Simplify the following difference quotients
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{ (5+h)^{2} - 125 }{ h }\]
anonymous
  • anonymous
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: \[h + 10 - (1/h)100\]
anonymous
  • anonymous
The answer in the text is \[75 + 15h + h ^{2}\]

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anonymous
  • anonymous
is this calculus or math analysis?
anonymous
  • anonymous
calculus!
anonymous
  • anonymous
do you have a sample from the book...my understanding of difference equations deals with circuits. i may not be able to assist you.
anonymous
  • anonymous
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
anonymous
  • anonymous
do you have the original function?
anonymous
  • anonymous
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 \[(f(x+h) -f(x))/h) = (x^2 + 2 xh + h^2)/h\]
anonymous
  • anonymous
the answer would 2x as h approaches zero.
anonymous
  • anonymous
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
anonymous
  • anonymous
It's alright, i was planning on asking a teacher when I go to school
anonymous
  • anonymous
no worries....i think it's best.

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