Let $ f: R \rightarrow R$ be defined as $f(x)=\left\{\begin{array}{cc}\frac{\lambda | x^{2}-5 x+6|}{\mu\left(5 x-x^{2}-6\right)} & , x2 \\mu & , x=2\end{array}\right.$ Where $ [x] $ is the greatest integer less than or equal to $ x $. If $ f $ is continuous at $ x=2 $, then $ \lambda+\mu $ is equal to [JEE Main 2021, 25 Jul (Shift 1)]

Question

Let $ f: R \rightarrow R$ be defined as $f(x)=\left\{\begin{array}{cc}\frac{\lambda | x^{2}-5 x+6|}{\mu\left(5 x-x^{2}-6\right)} & , x<2 \e^{\frac{\tan (x-2)}{x-[x]}} & , x>2 \\mu & , x=2\end{array}\right.$ Where $ [x] $ is the greatest integer less than or equal to $ x $. If $ f $ is continuous at $ x=2 $, then $ \lambda+\mu $ is equal to [JEE Main 2021, 25 Jul (Shift 1)]

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Let \( f: R \rightarrow R\) be defined as \(f(x)=\left\{\begin{array}{cc}\frac{\lambda | x^{2}-5 x+6|}{\mu\left(5 x-x^{2…

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