Question

07* Calculate the limits

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

infinity
-infinity
3
1​

Answer 1

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.