Step 1 :Given the function F(x) = -4x^2 + 20x + 150, we need to find the limit of the function \(\frac{F(x)}{x-5}\) as x approaches 5.
Step 2 :Using the given function, we substitute it into the limit expression: \(\lim_{x \to 5} \frac{-4x^2 + 20x + 150}{x-5}\)
Step 3 :As x approaches 5, the denominator approaches 0, and the limit becomes undefined. Therefore, the limit of the function \(\frac{F(x)}{x-5}\) as x approaches 5 is \(\boxed{\infty}\)