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Limits Continuity and Differentiability question

2024 · 27 Jan · Shift 1 · Q39

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JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 27 Jan · Shift 1 · Q39

Limits Continuity and Differentiability question

2024 · 27 Jan · Shift 1 · Q39

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Consider the function.

f(x)=\left\{\begin{array}{cc} \frac{\mathrm{a}\left(7 x-12-x^2\right)}{\mathrm{b}\left|x^2-7 x+12\right|} & , x3 \\\\ \mathrm{~b} & , x=3, \end{array}\right.

where

[x]

denotes the greatest integer less than or equal to

x

. If

\mathrm{S}

denotes the set of all ordered pairs (a, b) such that

f(x)

is continuous at

x=3

, then the number of elements in

\mathrm{S}

is :

A
Infinitely many
B
4
C
2
D
1

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