If f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩3(1+|tanx|)α|tanx|,−12<x<0β,x=03(1+∣∣∣sinx3∣∣∣)6|sinx|,0<x<23 is continuous at x=0, then the ordered pair (α,β) is equal to

If f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪�

1.	If f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩3(1+\|tanx\|)α\|tanx\|,−12<x<0β,x=03(1+∣∣∣sinx3∣∣∣)6\|sinx\|,0<x<23 is continuous at x=0, then the ordered pair (α,β) is equal to
Answer» If $f (x) = ⎧ ⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎩ \begin{matrix} 3 (1 + \| tan x \|)^{\frac{α}{\| tan x \|}}, & - \frac{1}{2} < x < 0 β, & x = 0 3 {(1 + ∣ ∣ ∣ \frac{sin x}{3} ∣ ∣ ∣)}^{\frac{6}{\| sin x \|}}, & 0 < x < \frac{2}{3} \end{matrix}$ is continuous at $x = 0,$ then the ordered pair $(α, β)$ is equal to