PG entrance exam IIT JAM 2025 Mock Test Mathematical Science Analysis Continuity & Differentiability
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 \(\displaystyle\lim_{h \rightarrow 0^+}\)θ(h) is equal to __________.
Enter numerical value using the virtual keypad. Round off where necessary.