Let $f(x) = \begin{cases} \{1 + |\sin x|\}^{\pi/|\sin x|}, & -\pi/6 < x < 0 \\ e^{\tan 2x/\tan 3x}, & 0 < x < \pi/6 \end{cases}$ …

Mathematics

Problem

Let

f(x) = \begin{cases} \{1 + |\sin x|\}^{\pi/|\sin x|}, & -\pi/6 < x < 0 \\ e^{\tan 2x/\tan 3x}, & 0 < x < \pi/6 \end{cases}

Determine

a

and

b

such that

f(x)

is continuous at

x = 0