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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Differentiation

JEE Main · Mathematics · Differentiation

The valuc of f(4)-f(3) is

The valuc of f(4)−f(3)f(4)-f(3) is

Options

  1. AΔf(2)+Δ2f(1)+Δ3f(1)\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)
  2. BΔf(3)+Δ2f(2)+Δ3f(1)\Delta f(3)+\Delta^{2} f(2)+\Delta^{3} f(1)
  3. CΔf(2)+Δ2f(1)+Δ3f(0)\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(0)
  4. DNone of the above

Correct answer

A. Δf(2)+Δ2f(1)+Δ3f(1)\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)

Step-by-step solution

f(4)−f(3)=Δf(3)=Δ[f(2)+Δf(2)][∵Δf(2)=f(3)−f(2)]=Δf(2)+Δ2f(2)=Δf(2)+Δ2[f(1)+Δf(1)]=Δf(2)+Δ2f(1)+Δ3f(1)f(4)-f(3)=\Delta f(3)=\Delta[f(2)+\Delta f(2)][\because \Delta f(2)=f(3)-f(2)]=\Delta f(2)+\Delta^{2} f(2)=\Delta f(2)+\Delta^{2}[f(1)+\Delta f(1)]=\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)
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