Question

Given that, limₓ→ₐ f(x) = 0

limₓ→ₐ g(x) = 0
limₓ→ₐ h(x) = 1
limₓ→ₐ p(x) = [infinity]
limₓ→ₐ q(x) = [infinity],
Evaluate the limits below where possible.
(a) limₓ→ₐ [f(x)]ᵍ⁽ˣ⁾

Answer 1

To evaluate the limit limₓ→ₐ [f(x)]ᵍ⁽ˣ⁾, you can use the property that if the limits of two functions exist as x approaches a, you can take the limit of the product of those functions.

Step-by-step explanation:

To evaluate the limit limₓ→ₐ [f(x)]ᵍ⁽ˣ⁾, we can use the property that if the limits of two functions exist as x approaches a, we can take the limit of the product of those functions. That is, if limₓ→ₐ f(x) = L and limₓ→ₐ g(x) = M, then limₓ→ₐ (f(x) * g(x)) = L * M.

In this case, we are given that limₓ→ₐ f(x) = 0 and limₓ→ₐ g(x) = 0. Therefore, using the property mentioned earlier, we can say that limₓ→ₐ [f(x)]ᵍ⁽ˣ⁾ = 0 * 0 = 0.