Let $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {{x^2}}&{{\text{if}}}&{x 3} \end{array}} \right.$ Which one of the following is not correct?

$\lim _{x \rightarrow 2} f(x)=4$

$\lim _{x \rightarrow 3} f(x)=2$

$\lim _{x \rightarrow 4} f(x)=4$

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JEE MATHEMATICS MCQ: LIMITS

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Let

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {{x^2}}&{{\text{if}}}&{x < 1} \\ {x + 2}&{{\text{if}}}&{1 \leqslant x \leqslant 2} \\ {8 - 2x}&{{\text{if}}}&{2 < x \leqslant 3} \\ {2x - 4}&{i{\text{f}}}&{x > 3} \end{array}} \right.

Which one of the following is not correct?

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Correct option: A

\lim _{x \rightarrow 1} f(x)=1

Option A is correct because the left-hand limit at x=1 is 1, but the right-hand limit is 3, therefore the limit does not exist, making the statement incorrect.

JEE MATHEMATICS MCQ: LIMITS

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