anonymous
  • anonymous
difference quotient of function f(x) is defined as : f(x+h) - f(x)/ h compute the difference quotient of the given functions a) y(z) = 1/ z+2 b) g(x)= 6-x^2 please help
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
the h is the denominator
anonymous
  • anonymous
I think it should be [f(x+h) - f(x)/ ]h instead of f(x+h) - f(x)/ h
anonymous
  • anonymous
I am sorry for the typos I meant "I think it should be [f(x+h) - f(x) ]/h instead of f(x+h) - f(x)/ h"

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anonymous
  • anonymous
yeah iamignorant
anonymous
  • anonymous
y(z +h) -y(z)= 1/(z+h+2) - 1/(z+2)= z+2-z-h-2/(z+h+2)(z+2) = -h/(z+h+2)(z+2) dividing by h on both sides gives y(z +h) -y(z)/h = 1/(z+h+2)(z+2)
anonymous
  • anonymous
oh i missed the negative sign in the numerator :)
anonymous
  • anonymous
g(x) = 6 - x^2 g(x+h) = 6-(x +h)^2= 6-x^2-2xh- h^2 g(x+h) - g(x) = -2xh - h^2 = -h(2x +h) g(x+h) - g(x)/h = 2x +h
anonymous
  • anonymous
do u mind explaining the y(z+h)-y(z) blablabla how it comes about?
anonymous
  • anonymous
replace z by z +h
anonymous
  • anonymous
then simlify the expression by taking the LCM

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