GATE 2024 ST – Question 47

Calculus · Single Variable Calculus · 2 marks · Multiple select

1. F(x)=∫₀ˣf(t)dt on [0,2] is differentiable on (0,2).
2. For any ten points x₁,…,x₁₀ there is x₀ with f(x₀)=[Σf(x_i)]/10.
3. f is bounded on [−2,2].
4. If f is differentiable at 0 and f(0)=0, then lim_(x→0)[f(x)+f(x/2)+⋯+f(x/10)]/x=10f′(0).

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