# How do you find #lim (3+2sqrtu)/(4-sqrtu)# as #u->oo#?

# lim_(u rarr oo)(3+2sqrt(u))/(4-sqrt(u)) = -2 #

We can manipulate the limit as follows;

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To find the limit of (3+2√u)/(4-√u) as u approaches infinity, we can use the concept of rationalizing the denominator. By multiplying both the numerator and denominator by the conjugate of the denominator, which is (4+√u), we can simplify the expression.

After multiplying, we get: [(3+2√u)(4+√u)] / [(4-√u)(4+√u)]

Expanding the numerator and denominator, we have: (12 + 7√u + 2u) / (16 - u)

As u approaches infinity, the terms involving √u and u will dominate the expression. Since the highest power of u is in the numerator, we can ignore the denominator.

Therefore, the limit of (3+2√u)/(4-√u) as u approaches infinity is ∞.

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