Let f:R→R be defined asf(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩λ|x2−5x+6|μ(5x−x2−6),x<2e tan(x−2)x−[x],x>2 μ ,x=2where [x] is the greatest integer less than or equal to x. If f is continuous at x=2, then λ+μ is equal to

Let f:R→R be defined asf(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨�

1.	Let f:R→R be defined asf(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩λ\|x2−5x+6\|μ(5x−x2−6),x<2e tan(x−2)x−[x],x>2 μ ,x=2where [x] is the greatest integer less than or equal to x. If f is continuous at x=2, then λ+μ is equal to
Answer» Let $f : R \to R$ be defined as $f (x) = ⎧ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎩ \begin{matrix} \frac{λ \| x^{2} - 5 x + 6 \|}{μ (5 x - x^{2} - 6)}, & x < 2 e^{\frac{tan (x - 2)}{x - [x]}}, & x > 2 μ, & x = 2 \end{matrix}$ where $[x]$ is the greatest integer less than or equal to $x$ . If $f$ is continuous at $x = 2,$ then $λ + μ$ is equal to