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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Limits

NDA 2023 · Mathematics · Limits

Let f(x)=\ array cc a x(x+1)+b, & x < 1 x-1 & 1 ≤ x ≤ 2 array ....

Let f(x)=\left\{ax(x+1)+b,x<1x−11≤x≤2\begin{array}{cc}a x(x+1)+b, & x < 1 \\ x-1 & 1 \leq x \leq 2\end{array}\right. What is lim⁡x→0f(x)\lim _{x \rightarrow 0} f(x) equal to?

Options

  1. A−13-\frac{1}{3}
  2. B−23-\frac{2}{3}
  3. C0
  4. D1

Correct answer

B. −23-\frac{2}{3}

Step-by-step solution

Since, lim⁡x→0f(x)=lim⁡x→0ax(x+1)+b=b=−23\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} a x(x+1)+b=b=\frac{-2}{3}
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