Question

H(x) = f(x)/x² limₓ→∾ h(x) =

a) 0
b) [infinity]
c) 1
d) The limit does not exist

Answer 1

The limit of h(x) = f(x)/x² as x approaches infinity is 0, because f(x) represents a constant and the denominator increases without bound, making the fraction approach zero.

The correct answer is a.

Step-by-step explanation:

The student asked about the limit of the function h(x) = f(x)/x² as x approaches infinity. To determine the limit, let's consider the information provided.

Since f(x) is described as a horizontal line when 0 ≤ x ≤ 20, this implies that f(x) is a constant function. Let's denote this constant by C (even though the exact value isn't stated, it won't affect the limit to infinity). Hence, h(x) can be rewritten as h(x) = C/x². Now as x approaches infinity, the denominator x² increases without bound.

The value C/x² gets smaller and smaller as x gets larger, approaching zero. Therefore, the limit of h(x) as x approaches infinity is 0. This corresponds to option a) 0.