Q214 / 270 · NDA 2023 (Phase 2) · Mathematics

Let $f(x)=\left\{\begin{array}{cc}a x(x+1)+b, & x \lt 1 \\ x-1 & 1 \leq x \leq 2\end{array}\right.$ What is $\lim _{x \rightarrow 0} f(x)$ equal to?

  • A
    $-\frac{1}{3}$
  • Correct answer
    B
    $-\frac{2}{3}$
  • C
    0
  • D
    1

Solution

Since, $\lim _{x \rightarrow 0} f(x)$ $=\lim _{x \rightarrow 0} a x(x+1)+b=b=\frac{-2}{3}$

Hence, the correct answer is option: 'B'.

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