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anonymous
 4 years ago
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))/(xa)
x>a
Also what does this relate to:
y = f'(a) (xa) + f(a)
anonymous
 4 years ago
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))/(xa) x>a Also what does this relate to: y = f'(a) (xa) + f(a)

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0To make it clear I understand that the first equation is the definition of the derivative, where does the second formula come from?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0they are identical, they just look different. take the second one, replace \[xa\] by \[h\] and you will see that there is no difference

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[h\] and \[xa\] 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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