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Limits Continuity and Differentiability question

2021 · 25 Jul · Shift 1 · Q27

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 25 Jul · Shift 1 · Q27

Limits Continuity and Differentiability question

2021 · 25 Jul · Shift 1 · Q27

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let f : R

\to

R be defined as

f(x) = \left\{ {\begin{matrix} {{{\lambda \left| {{x^2} - 5x + 6} \right|} \over {\mu (5x - {x^2} - 6)}},} & {x \lt 2} \\ {{e^{{{\tan (x - 2)} \over {x - [x]}}}},} & {x \gt 2} \\ {\mu ,} & {x = 2} \\ \end{matrix} } \right.

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 :

A
e( $-$ e + 1)
B
e(e $-$ 2)
C
1
D
2e $-$ 1

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