Mathematics

Problem

The function

g

is defined by

g(x)=\begin{cases} \displaystyle \dfrac{\sin ax}{x}, & x<0,\\ bx^{2}+1, & x\ge 0. \end{cases}

For which value of

a

does

\displaystyle \lim_{x\to 0} g(x)

exist and equal

1

? a)

\dfrac{\pi}{2}

1

0

2