Question

$\lim_{x \leftarrow 0} \frac{x^2}{sin(x^2)cos(x)}$

Answer 1

1

Answer 2

The limit is of the form 0/0. Rewrite the expression as a product $\frac{x^2}{\sin(x^2)} \cdot \frac{1}{\cos(x)}$. Use the standard limit $\lim_{y \to 0} \frac{y}{\sin(y)} = 1$ for the first term by substituting $y=x^2$. Evaluate the limit of the second term $\frac{1}{\cos(x)}$ by direct substitution as $x \to 0$. The limit of the product is the product of the limits.