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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Limits

NDA 2015 · Mathematics · Limits

Consider the function f(x)=\ array ccc (α x)/(π-2 x) & If & x ≠...

Consider the function f(x)=\left\{αcos⁡xπ−2x If x≠π23 If x=π2\begin{array}{ccc} \frac{\alpha \cos x}{\pi-2 x} & \text{ If } & x \neq \frac{\pi}{2} \\ 3 & \text{ If } & x=\frac{\pi}{2} \end{array}\right. Which is continuous at x=π2x=\frac{\pi}{2}, where α\alpha is a constant. What is lim⁡x→0f(x)\lim _{x \rightarrow 0} f(x) equal to?

Options

  1. A0
  2. B3
  3. C3π\frac{3}{\pi}
  4. D6π\frac{6}{\pi}

Correct answer

D. 6π\frac{6}{\pi}

Step-by-step solution

lim⁡x→0f(x)=αcos⁡xπ−2x=α(cos⁡0)π−2(0)=6π\begin{aligned} & \lim _{x \rightarrow 0} f(x)=\frac{\alpha \cos x}{\pi-2 x} \\ & =\frac{\alpha(\cos 0)}{\pi-2(0)}=\frac{6}{\pi}\end{aligned}\therefore \quad$ Option (D) is correct.
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