Question

Let f(x) = $\sqrt[3]{x}$ for x ∈ (0, ∞), and θ(h) be a function such that
f(3 + h) − f(3) = hf′ (3 + θ(h)h)
for all h ∈ (−1, 1). Then $\lim\limits_{h→0} θ(h)$ is equal to _________. (rounded off to two decimal places)

Answer 1

The correct answer is 0.49 to 0.51. (approx)