Question

The value of $\left(\frac{{\Delta }^2}{E}\right)x^3$ at $h=1$ is

• A. $8x$
• B. $6x$
• C. $5x^2$
• D. $6x^2$

Answer 1

Answer: (B)

$6x$

$\left(\frac{{\Delta }^2}{E}\right)x^3=\left(\frac{(E-1{)}^2}{E}\right)x^3$
$=\left(\frac{E^2-2E+1}{E}\right)x^3$
$=E\left(x^3\right)-2x^3+E^{-1}\left(x^3\right)$
$=(x+1{)}^3-2x^3+(x-1{)}^3$
$=x^3+1+3x^2+3x-2x^3+x^3-1-3x^2+3x$
$=6x$