# How do you find #lim (1+5/sqrtu)/(2+1/sqrtu)# as #u->0^+# using l'Hospital's Rule?

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# lim_(u rarr 0^+) (1+5/sqrt(u))/(2+1/sqrt(u)) = 5 #

We do not need to apply L'Hôpital's as this is a trivial limit to evaluate:

Whereas:

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To find ( \lim_{u \to 0^+} \frac{1 + \frac{5}{\sqrt{u}}}{2 + \frac{1}{\sqrt{u}}} ) using L'Hôpital's Rule:

- Notice that as ( u \to 0^+ ), both the numerator and denominator approach ( \infty ).
- Apply L'Hôpital's Rule by taking the derivative of the numerator and denominator separately with respect to ( u ).
- Differentiate the numerator and denominator and simplify.
- Evaluate the limit of the resulting expression as ( u \to 0^+ ).
- The resulting value is the limit of the original expression.

By applying L'Hôpital's Rule, you can find the limit of the given expression as ( u ) 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.

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