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 $\sin(x)$.