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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Limits

NDA 2010 · Mathematics · Limits

What is value of _ x arrow 0 ( (a x)- (b x))/(x^2)

What is value of lim⁡x→0cos⁡(ax)−cos⁡(bx)x2\lim _{x \rightarrow 0} \frac{\cos (a x)-\cos (b x)}{x^2}

Options

  1. Aa−ba-b
  2. Ba+ba+b
  3. Cb2−a22\frac{b^2-a^2}{2}
  4. Db2+a22\frac{b^2+a^2}{2}

Correct answer

C. b2−a22\frac{b^2-a^2}{2}

Step-by-step solution

Using L'Hospital rule lim⁡x→0−asin⁡ax+bsin⁡bx−2xlim⁡x→0−a2cos⁡ax+b2cos⁡bx2=b2−a22\begin{aligned} & \lim _{x \rightarrow 0} \frac{-a \sin a x+b \sin b x}{-2 x} \\ & \lim _{x \rightarrow 0} \frac{-a^2 \cos a x+b^2 \cos b x}{2} \\ & =\frac{b^2-a^2}{2} \end{aligned}
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