# Given the function #f(x)=-3-x#, how do you express the value of #(f(x+h)-f(x))/h#?

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See explanation.

Combining the two expressions we get:

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To express the value of ((f(x+h)-f(x))/h) for the function (f(x)=-3-x), we substitute (f(x+h)) and (f(x)) into the expression:

[ \frac{f(x+h)-f(x)}{h} = \frac{(-3-(x+h))-(-3-x)}{h} ]

Now, simplify the expression:

[ \frac{(-3-x-h)-(-3-x)}{h} = \frac{-3-x-h+3+x}{h} = \frac{-h}{h} ]

Finally, cancel out (h) in the numerator and denominator:

[ \frac{-h}{h} = -1 ]

So, the value of ((f(x+h)-f(x))/h) for the given function is (-1).

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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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