# How do you find the limit #(x+5)(1/(2x)+1/(x+2))# as #x->0^+#?

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To find the limit of the expression (x+5)(1/(2x)+1/(x+2)) as x approaches 0 from the positive side, we can simplify the expression first. By multiplying the terms, we get (x+5)(1/(2x)+1/(x+2)) = (x+5)(x+2+2x)/(2x(x+2)). Simplifying further, we have (x+5)(3x+2)/(2x(x+2)).

Now, we can evaluate the limit by substituting 0 for x in the simplified expression. Plugging in x=0, we get (0+5)(3(0)+2)/(2(0)(0+2)). Simplifying this, we have 5(2)/(0), which is undefined. Therefore, the limit of the expression as x approaches 0 from the positive side does not exist.

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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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