Statement 1: `lim_(xto0)[(sinx)/x]=0`
Statement 2: `lim_(xto0)[(sinx)/x]=1`

Options

A. Statement-1 is True, Statement -2 is True, Statement -2 is True and Statement -2 is a correct explanation for statement -1.
B. Statement -1 is True, Statement -2 is True and Statement -2 is Not is a correct explanation for Statement -1.
C. Statement -1 is True, Statement -2 is False.
D. Statement -1 is False, Statement -2 is True.

Answer

To solve the problem, we need to evaluate the two statements regarding the limit of \(\frac{\sin x}{x}\) as \(x\) approaches 0.

### Step-by-Step Solution:

**Step 1: Understand the limit.**
We need to evaluate:
\[ \lim_{x \to 0} \frac{\sin x}{x} \]

**Hint:** Recall that this limit is a well-known limit in calculus.

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**Step 2: Apply L'Hôpital's Rule.**
Since both the numerator and denominator approach 0 as \(x\) approaches 0, we can apply L'Hôpital's Rule:
\[ \lim_{x \to 0} \frac{\sin x}{x} = \lim_{x \to 0} \frac{\cos x}{1} \]

**Hint:** L'Hôpital's Rule is used when you encounter the indeterminate form \(\frac{0}{0}\).

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**Step 3: Evaluate the limit using L'Hôpital's Rule.**
Now, substituting \(x = 0\) into the derivative:
\[ \lim_{x \to 0} \cos x = \cos(0) = 1 \]

**Hint:** Remember that \(\cos(0) = 1\).

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**Step 4: Conclude the evaluation.**
Thus, we have:
\[ \lim_{x \to 0} \frac{\sin x}{x} = 1 \]

**Hint:** This confirms that the limit approaches 1, not 0.

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**Step 5: Analyze the statements.**
- Statement 1: \(\lim_{x \to 0} \frac{\sin x}{x} = 0\) (False)
- Statement 2: \(\lim_{x \to 0} \frac{\sin x}{x} = 1\) (True)

**Hint:** Compare the results of the limit with the statements given.

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### Final Conclusion:
The correct statement is Statement 2, which is true, while Statement 1 is false.