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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Limits

NTA Abhyas 2020 · Mathematics · Limits

The value of _ x → ∞ (ln x) ^ 2 2 + 3x^ 2 is equal to

The value of lim⁡x→∞(lnx)22+3x2\lim_{x \to \infty}\dfrac{{\left(ln x\right)}^{2}}{2 + 3x^{2}} is equal to

Options

  1. A13\dfrac{1}{3}
  2. B23\dfrac{2}{3}
  3. C11
  4. D00

Correct answer

D. 00

Step-by-step solution

By L-hospital rule,
lim⁡x→∞2(lnx).1x6x\lim_{x \to \infty}\dfrac{2\left(ln x\right). \dfrac{1}{x}}{6x}
⇒lim⁡x→∞lnx3x2⇒ \lim_{x \to \infty}\dfrac{ln x}{3x^{2}}
Again by L-hospital rule,
lim⁡x→∞1x6x⇒lim⁡x→∞16x2=0\lim_{x \to \infty}\dfrac{\dfrac{1}{x}}{6x} ⇒ \lim_{x \to \infty}\dfrac{1}{6x^{2}} = 0
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