# What is #lim_ (xrarr0) (1/x -1/x^2-x)#?

Since both limits from left and right are

Thus, we have to add up the two fractions:

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The limit of (1/x - 1/x^2 - x) as x approaches 0 is 0.

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To find ( \lim_{x \to 0} \left(\frac{1}{x} - \frac{1}{x^2 - x}\right) ), you can simplify the expression first by finding a common denominator for the two fractions, then combine them into a single fraction. Once simplified, you can directly substitute ( x = 0 ) into the expression to evaluate the limit.

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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.

- How do you find the limit of #((root3 x) -1)/((sqrt x) -1)# as x approaches 1?
- How do you determine the limit of #[(n+5)/(n-1)]^n# as n approaches #oo#?
- How do you evaluate #( ( x / (x-1 ) - (1 / lnx ) )# as x approaches 1+?
- How do you find #lim (y+1)/((y-2)(y-3))# as #x->3^+#?
- How do you find the limit of #sqrt(x^2- 3x)# as x approaches 3?

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