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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
If $f(x) = \left\{ \begin{array}{l}{x^2} - 3,\;2 < x < 3\\2x + 5,\;3 < x < 4\end{array} \right.$, the equation whose roots are $\mathop {\lim }\limits_{x \to {3^ - }} f(x)$ and $\mathop {\lim }\limits_{x \to {3^ + }} f(x)$ is
  • A
    ${x^2} - 7x + 3 = 0$
  • B
    ${x^2} - 20x + 66 = 0$
  • ✓
    ${x^2} - 17x + 66 = 0$
  • D
    ${x^2} - 18x + 60 = 0$
✓

Answer

Correct option: C.
${x^2} - 17x + 66 = 0$
c
(c) $f(x) = \left\{ \begin{array}{l}{x^2} - 3,\,\,2 < x < 3\\2x + 5,\,3 < x < 4\end{array} \right.$

$\mathop {\lim }\limits_{x \to {3^ - }} f(x) = \mathop {\lim }\limits_{x \to {3^ - }} ({x^2} - 3) = 6$

and $\mathop {\lim }\limits_{x \to {3^ + }} f(x) = \mathop {\lim }\limits_{x \to {3^ + }} (2x + 5) = 11$

Hence, the required equation will be

${x^2} - $ (sum of roots) $x + $ (Product of roots) = $0$

$i.e.,$ ${x^2} - 17x + 66 = 0$.

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