()) If \( \lim _{x \rightarrow-5} f(x)^{\cdot}=-3 \) and \( \lim _{x \rightarrow-5} g(x)=-10 \), what is \( \lim _{x \rightarrow-5}\left([f(x)]^{2} g(x)\right) \) ?

To find the limit \( \lim _{x \rightarrow -5} \left([f(x)]^{2} g(x)\right) \), we can utilize the properties of limits. Given that \( \lim _{x \rightarrow -5} f(x) = -3 \) and \( \lim _{x \rightarrow -5} g(x) = -10 \), we can compute the limit of the expression: 1. First, calculate \( \lim _{x \rightarrow -5} [f(x)]^2 \): \[ \lim _{x \rightarrow -5} [f(x)]^2 = \left(\lim _{x \rightarrow -5} f(x)\right)^{2} = (-3)^{2} = 9. \] 2. Next, we have \( \lim _{x \rightarrow -5} g(x) = -10 \). 3. Now, we can combine these results: \[ \lim _{x \rightarrow -5} \left([f(x)]^{2} g(x)\right) = \lim _{x \rightarrow -5} [f(x)]^2 \cdot \lim _{x \rightarrow -5} g(x) = 9 \cdot (-10) = -90. \] Thus, the final result is: \[ \lim _{x \rightarrow -5} \left([f(x)]^{2} g(x)\right) = -90. \]