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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2018 · Mathematics · Continuity and Differentiability

If f(x)=(x^2-9)/(x^2-2 x-3), x ≠ 3 is continuous at x=3 , then...

If f(x)=x2−9x2−2x−3,x≠3f(x)=\frac{x^2-9}{x^2-2 x-3}, x \neq 3 is continuous at x=3x=3, then which one of the following is correct?

Options

  1. Af(3)=0f(3)=0
  2. Bf(3)=1.5f(3)=1.5
  3. Cf(3)=1.5f(3)=1.5
  4. Df(3)=−1.5f(3)=-1.5

Correct answer

B. f(3)=1.5f(3)=1.5

Step-by-step solution

f(x)=x2−9x2−2x−3f(x)=\frac{x^2-9}{x^2-2 x-3} Given, the function is continuous at x=3\mathrm{x}=3. f(3)=lim⁡x→3x2−9x2−2x−3=lim⁡x→3(x+3)(x−3)(x−3)(x+1)=3+33+1=64=32=1.5\begin{aligned} & f(3)=\lim _{x \rightarrow 3} \frac{x^2-9}{x^2-2 x-3} \\ & =\lim _{x \rightarrow 3} \frac{(x+3)(x-3)}{(x-3)(x+1)} \\ & =\frac{3+3}{3+1}=\frac{6}{4}=\frac{3}{2}=1.5 \end{aligned}
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