# How do you evaluate # [ (1/x) - (1/(x^(2)+x) ) ]# as x approaches 0?

Have a look at this Solution that doesn't uses L'Hospital's Rule :

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Combine the fractions

Now let's use L'Hospital's Rule

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To evaluate the expression [(1/x) - (1/(x^2+x))] as x approaches 0, we can simplify it by finding a common denominator and combining the fractions. The common denominator is x(x+1). Simplifying the expression gives us [(x+1 - x) / (x(x+1))]. The numerator simplifies to 1, and the denominator becomes x(x+1). As x approaches 0, the expression evaluates to 1 / (0(0+1)), which simplifies to 1 / 0. However, division by zero is undefined, so the expression is undefined as x approaches 0.

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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 #sin (x^2)/sin^2(2x)# as x approaches 0?
- How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ?
- How do you find the limit of #(3x^2-x-10)/(x^2+5x-14)# as x approaches 2?
- How do you evaluate the limit #(x^2-25)/(x+5)# as x approaches #-5#?
- How do you find the limit of # (4t – 2t)/(t) # as t approaches 0?

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