anonymous
  • anonymous
Can someone explain to me the difference and application of the two formulas lim (f(x+h) - f(x))/h h->0 lim (f(x) - f(a))/(x-a) x->a Also what does this relate to: y = f'(a) (x-a) + f(a)
Calculus1
katieb
  • katieb
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anonymous
  • anonymous
To make it clear I understand that the first equation is the definition of the derivative, where does the second formula come from?
anonymous
  • anonymous
they are identical, they just look different. take the second one, replace \[x-a\] by \[h\] and you will see that there is no difference
anonymous
  • anonymous
\[h\] and \[x-a\] are both different ways of expressing the change in x for the secant line of a function. The first equation shows the limit of the function as the change of x tends directly to zero. The second function shows the limit of the function as x tends to a; as x gets really close to a, the change in x also approaches zero. They are the same function, one just uses a new variable (h) to describe the change in x.

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