# $$\rm \displaystyle \lim_{x \rightarrow \infty} 2x \sin \left(\frac{4} {x}\right)$$ का मान ज्ञात कीजिए।

1. 2
2. 4
3. 8
4. $$\frac 1 2$$

Option 3 : 8
Free
CRPF Head Constable Ministerial 22 Feb 2023 (Shift 1) Memory-Based Test
1.3 Lakh Users
100 Questions 100 Marks 90 Mins

## Detailed Solution

संकल्पना:

$$\rm \displaystyle \lim_{x \rightarrow 0} \frac{\sin x}{x} = 1$$

गणना:

$$\rm \displaystyle \lim_{x \rightarrow \infty} 2x \sin \left(\frac{4} {x}\right)$$

$$\rm 2 \times \displaystyle \lim_{x → ∞} \frac{\sin \left(\frac{4} {x}\right)}{\left(\frac{1}{x} \right )}$$

$$\rm 2 \times \displaystyle \lim_{x → ∞} \frac{\sin \left(\frac{4} {x}\right)}{\left(\frac{4}{x} \right )} \times 4$$

माना कि $$\rm \frac {4}{x} = t$$ है।

यदि x → ∞ है, तो t → 0 है।

$$\rm 8 \times\displaystyle \lim_{t \rightarrow 0} \frac{\sin t}{t}$$

= 8 × 1

= 8
The text passage contains a mathematical question in the form of a limit problem, followed by multiple-choice options, and a detailed solution that leads to the correct answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# $$\rm \displaystyle \lim_{x \rightarrow \infty} 2x \sin \left(\frac{4} {x}\right)$$ का मान ज्ञात कीजिए।

1. 2
2. 4
3. 8
4. $$\frac 1 2$$

Option 3 : 8
Free
CRPF Head Constable Ministerial 22 Feb 2023 (Shift 1) Memory-Based Test
1.3 Lakh Users
100 Questions 100 Marks 90 Mins

## Detailed Solution

संकल्पना:

$$\rm \displaystyle \lim_{x \rightarrow 0} \frac{\sin x}{x} = 1$$

गणना:

$$\rm \displaystyle \lim_{x \rightarrow \infty} 2x \sin \left(\frac{4} {x}\right)$$

$$\rm 2 \times \displaystyle \lim_{x → ∞} \frac{\sin \left(\frac{4} {x}\right)}{\left(\frac{1}{x} \right )}$$

$$\rm 2 \times \displaystyle \lim_{x → ∞} \frac{\sin \left(\frac{4} {x}\right)}{\left(\frac{4}{x} \right )} \times 4$$

माना कि $$\rm \frac {4}{x} = t$$ है।

यदि x → ∞ है, तो t → 0 है।

$$\rm 8 \times\displaystyle \lim_{t \rightarrow 0} \frac{\sin t}{t}$$

= 8 × 1

= 8
user
The text passage contains a mathematical question in the form of a limit problem, followed by multiple-choice options, and a detailed solution that leads to the correct answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER