Recall the definition of a derivative: f'(x)=f(x+∆x) - f(x) / ∆x Explain why, if the denominator ∆x is going to zero, the fraction f(x+∆x)−f(x) doesn’t necessarily ∆x go to infinity. (Hint: The numerator is also going to zero... so what’s the fraction doing?)

Step-by-step explanation:

Given the definition of a derivative: f'(x)=f(x+∆x) - f(x) / ∆x, if we take the limit as ∆x tends to zero, the derivative will become;

f'(x) = f(x+∆x) - f(x) / ∆x

f'(x) = f(x+0) - f(x) / 0

f'(x) = f(x) - f(x) / 0

Since f(x)-f(x) = 0, the derivative will become;

f'(x) = 0/0 (indeterminate)

As we can see, the derivative doesn't turn to infinity because the numerator of function also tends to zero as ∆x--> 0.

Instead of the fraction to tend to infinity, it becomes an indeterminate function and an indeterminate function can be solved further by applying l'hospital rule on the resulting function and re-substituting ∆x. There is possibility that the equation will give a finite value afterwards depending on the function.

we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .