Let a,b,c∈R such that a+b+c=π. If f(x)=⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩sin(ax2+bx+c)x2−1,if x<1−1,if x=1a sgn(x+1)cos(2x−2)+bx2,if 1<x≤2 is continuous at x=1, then the value of (a2+b2) is [Here, sgn(k) denotes signum function of k]

Let a,b,c∈R such that a+b+c=π. If f(x)=⎧⎪⎪⎪⎪⎨⎪⎪⎪�

1.	Let a,b,c∈R such that a+b+c=π. If f(x)=⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩sin(ax2+bx+c)x2−1,if x<1−1,if x=1a sgn(x+1)cos(2x−2)+bx2,if 1<x≤2 is continuous at x=1, then the value of (a2+b2) is [Here, sgn(k) denotes signum function of k]
Answer» Let $a, b, c \in R$ such that $a + b + c = π$ . If $f (x) = ⎧ ⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪ ⎩ \begin{matrix} \frac{sin (a x^{2} + b x + c)}{x^{2} - 1}, & if x < 1 - 1, & if x = 1 a sgn (x + 1) cos (2 x - 2) + b x^{2}, & if 1 < x \leq 2 \end{matrix}$ is continuous at $x = 1$ , then the value of $(a^{2} + b^{2})$ is [Here, $sgn (k)$ denotes signum function of $k$ ]