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07* Calculate the limits

(a) lim x→∞ (3x^7/2+7x^-1/2) / (x²-x^1/2)

infinity
-infinity
3
1​

User Veikedo
by
7.7k points

1 Answer

5 votes

The limit is


\displaystyle \lim_(x\to\infty) (3x^(7/2) + 7x^(-1/2))/(x^2 - x^(1/2)) = \lim_(x\to\infty) (3x^(3/2) + 7x^(-5/2))/(1 - x^(-3/2)) = \boxed{\infty}

since the degree of the numerator exceeds the degree of the denominator.

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