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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Limits

NDA 2022 · Mathematics · Limits

What is _ x arrow 0 x 1- ^4 x equal to?

What is lim⁡x→0x1−cos⁡4x\lim _{x \rightarrow 0} \frac{x}{\sqrt{1-\cos ^4 x}} equal to?

Options

  1. A122\frac{1}{2 \sqrt{2}}
  2. B−122-\frac{1}{2 \sqrt{2}}
  3. C2\sqrt{2}
  4. DLimit does not exist

Correct answer

D. Limit does not exist

Step-by-step solution

lim⁡x→0x1−cos⁡4x=lim⁡x→02x2∣sin⁡2x∣×12 L.H.L =−122 and  R.H.L. =122∵ L.H.L ≠ R.H.L. \begin{aligned} & \lim _{x \rightarrow 0} \frac{x}{\sqrt{1-\cos 4 x}}=\lim _{x \rightarrow 0} \frac{2 x}{\sqrt{2}|\sin 2 x|} \times \frac{1}{2} \\ & \text{ L.H.L }=-\frac{1}{2 \sqrt{2}} \text{\text{ and } R.H.L. }=\frac{1}{2 \sqrt{2}} \\ & \because \quad \text{ L.H.L } \neq \text{ R.H.L. } \end{aligned} So, lim⁡x→0f(x)\lim _{x \rightarrow 0} f(x) is not exist.
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