What is the lim of sin^2(x) when x approaches 0-

The limit of \( \sin^2(x) \) as \( x \) approaches 0 from the left is:

\[
\lim_{x \to 0^-} \sin^2(x) = 0
\]

Here's why:  
1. The function \( \sin(x) \) is continuous and symmetric around \( x = 0 \). It approaches 0 from both the left and the right as \( x \to 0 \).
2. Squaring the sine function, \( \sin^2(x) \), also tends to 0 as \( x \to 0 \) because \( (\sin(x))^2 = 0^2 = 0 \).

Thus, regardless of the direction (from the left or right), \( \sin^2(x) \) tends to 0 as \( x \) approaches 0.

### Do you want more details or have any questions?

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Here are five related questions:
1. What is the limit of \( \sin(x) \) as \( x \) approaches 0?
2. How does the behavior of \( \cos^2(x) \) compare as \( x \to 0 \)?
3. What happens to \( \sin^2(x) \) as \( x \) approaches \( \pi \)?
4. Can we generalize the behavior of \( \sin^n(x) \) as \( x \to 0 \) for any \( n \)?
5. How do we find the derivative of \( \sin^2(x) \)?

**Tip:** For small values of \( x \), \( \sin(x) \) behaves approximately like \( x \), which can be useful for evaluating limits involving \( \sin(x) \).

What is the lim of sin^2(x) when x approaches 0?

Explore the limit of sin^2(x) as x approaches 0, including detailed explanations using the continuity of the sine function and limit theorems. This trigonometry problem is suitable for Grades 10-12 students and offers insights into key limit concepts.

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