# Is there a difference between #lim_(h->0)(f(x+h)-f(x))/h# and #lim_(deltax->0)(f(x+deltax)-f(x))/(deltax)#?

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It is only a different notation.

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No, there is no difference between ( \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} ) and ( \lim_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x} ). Both expressions represent the derivative of ( f(x) ) with respect to ( x ) and are equivalent. The use of different variables (such as ( h ) and ( \Delta x )) is a matter of notation preference.

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No, there is no difference between ( \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} ) and ( \lim_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x} ). They both represent the derivative of the function ( f(x) ) with respect to ( x ), often denoted as ( f'(x) ) or ( \frac{df}{dx} ). They are different notations for the same concept of finding the rate of change of ( f(x) ) as the change in ( x ) approaches zero.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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