# How do you find the limit of #[(1/(x+1))-1]/x# as x approaches 0?

This expression can be rewritten like this

The limit will now be

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

[(1/(x+1))-1]/x can be rewritten as [(1-x-1)/(x+1)]/x, which simplifies to (-x/(x+1))/x.

Next, we can simplify further by multiplying the numerator and denominator by (1/x). This gives us -1/(x+1).

Finally, as x approaches 0, the expression -1/(x+1) approaches -1/1, which is equal to -1.

Therefore, the limit of [(1/(x+1))-1]/x as x approaches 0 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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