MHT CET · Maths · Differentiation
The value of \(\left(\frac{\Delta^{2}}{E}\right) x^{3}\) at \(h=1\) is
- A \(8 x\)
- B \(6 x\)
- C \(5 x^{2}\)
- D \(6 x^{2}\)
Answer & Solution
Correct Answer
(B) \(6 x\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} &\left(\frac{\Delta^{2}}{E}\right) x^{3}=\left(\frac{(E-1)^{2}}{E}\right) x^{3} \\ &=\left(\frac{E^{2}-2 E+1}{E}\right) x^{3} \\ &=E\left(x^{3}\right)-2 x^{3}+E^{-1}\left(x^{3}\right) \\ &=(x+1)^{3}-2 x^{3}+(x-1)^{3} \\ &=x^{3}+1+3 x^{2}+3 x-2 x^{3}+x^{3}-1-3 x^{2}+3 x \\ &=6 x \end{aligned}\)
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