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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
MCQ
What is the value of $\lim_{\text{y} \rightarrow 0}(32\text{x}^2 \text{cosec} ^2 4\text{x}) ?$
  • A
    $1$
  • B
    $4$
  • ✓
    $2$
  • D
    $3$
✓

Answer

Correct option: C.
$2$
he limit can be written as,
$\lim_{\text{x} \rightarrow 0}\frac{32\text{x}^2}{\sin^2 4\text{x}}$
$2\times\lim_\limits{\text{x} \rightarrow 0}\frac{4\text{x}}{\sin 4\text{x}}\times\ \lim_\limits{\text{x} \rightarrow 0}\frac{4\text{x}}{\sin 4\text{x}}$
$= 2 \times 1 \times 1$
$= 2$

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