If where and denotes greatest integer less than or equal to

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

k=\lim_{x\rightarrow 0^+}\left(\text{Min.}(t^2-6(t+x)+12)+\left[\frac{\ln(1+2x)}{x}\right]\right)

where

t\in\mathbb{R}

and

[y]

denotes greatest integer less than or equal to

y

, then the value of

\frac{3}{2}k

is equal to (a) 4 (b) 3 (c) 6 (d) 9