Question

If m = `lim_(x→∞) (ℓ na)^3/(1 + 2lnx + 3(lnx)^2 + 4(lnx)^3` then the value of 8 m is ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

If m = `lim_(x→∞) (ℓ na)^3/(1 + 2lnx + 3(lnx)^2 + 4(lnx)^3` then the value of 8 m is 2.00.

Explanation:

Put t = logx

as x→∞, t→∞

∴ Given limit m = `lim_(t→∞) t^3/(1 + 2t + 3t^2 + 4t^3) = 1/4`

∴ 8m = 2