QJEEM21Ma679b: JEE Main 2021 Mathematics - Class 12 JEEM21Ma679b Solution: Let f : R R be defined as f ( x ) = { λ

Question

Verified Solution • 2025–26 Session moderate

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 is than or equal to x. If f is continuous at x = 2, then

\lambda

+

\mu

is equal to :

Accepted Answer

\mathop {\lim }\limits_{x \to {2^ + }} f(x) = \mathop {\lim }\limits_{x \to {2^ + }} {e^{{{\tan (x - 2)} \over {x - 2}}}} = {e^1}

\mathop {\lim }\limits_{x \to {2^ - }} f(x) = \mathop {\lim }\limits_{x \to {2^ - }} {{ - \lambda (x - 2)(x - 3)} \over {\mu (x - 2)(x - 3)}} = - {\lambda \over \mu }

For continuity

\mu = e = - {\lambda \over \mu } \Rightarrow \mu = e,\lambda = - {e^2}

\lambda + \mu = e( - e + 1)

Step-by-Step Verified Solution