lim _(xarrow 0)(sin^25x)/(4x^2)

To find the limit of the given expression as approaches 0, we can use the standard limit .First, rewrite the given expression: We can split this into two parts: Next, use the identity \( \sin^2(5x) = (\sin(5x))^2 \): Now, apply the standard limit \( \lim_{x \to 0} \frac{\sin(5x)}{x} = 5 \): Therefore, the limit is: