# How do you find the limit of #(1/(x+4)-(1/4))/(x)# as #x->0#?

Find a common denominator within the fractions of the numerator:

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To find the limit of the expression (1/(x+4)-(1/4))/(x) as x approaches 0, we can simplify the expression first.

First, let's find a common denominator for the two fractions in the numerator. The common denominator is 4(x+4).

Next, we can combine the fractions in the numerator by subtracting them. This gives us ((4- (x+4))/(4(x+4)))/(x).

Simplifying further, we have (-x)/(4(x+4))/(x).

Now, we can simplify the expression by canceling out the x terms in the numerator and denominator. This leaves us with -1/(4(x+4)).

Finally, we can take the limit as x approaches 0. Plugging in 0 for x, we get -1/(4(0+4)) = -1/16.

Therefore, the limit of (1/(x+4)-(1/4))/(x) as x approaches 0 is -1/16.

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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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- For what values of x, if any, does #f(x) = 1/((x-9)(x-1)(x-3)) # have vertical asymptotes?

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