If f ' is continuous, f(5) = 0, and f '(5) = 7, evaluate lim x→0
f(5 + 5x) + f(5 + 6x)
x

An indeterminate form is an expression involving two functions whose limit cannot be determined solely from the limits of the individual functions.

After evaluation,

Here, given that, f(5) = 0, and f '(5) = 7

We have to find,

When substituting the limit x=0. We get 0/0 form which is indeterminate form.

So, Here we use L'Hospital's rule, because direct substitution of a limit yields an indeterminate form.

Substituting the value of f '(5) = 7 in above equation.

             =

Thus,

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Correct question is;

If f ' is continuous, f(5) = 0, and f '(5) = 7, evaluate;

lim x→0 [f(5 + 5x) + f(5 + 6x)]/x

The limit is 77

Step-by-step explanation:

Since we want to evaluate;

lim x→0 [f(5 + 5x) + f(5 + 6x)]/x

Thus, let's plug in 0 for x to get;

lim x→0 [f(5 + 5x) + f(5 + 6x)]/x = [f(5) + f(5)]/0

Since we are told that f(5) = 0, thus we now have;

[f(5) + f(5)]/0 = 0/0

Since, we have a limit of both numerator and denominator as 0,thus let's apply L'Hospital's Rule which states that: if we have an indeterminate form of 0/0 or ∞/∞, we will differentiate the numerator and differentiate the denominator and then take the limit.

Thus, applying L'Hospital's rule and using chain rule in differentiating, we have;

lim x→0 [5f'(5 + 5x) + 6f'(5 + 6x)]/1 = 5f'(5) + 6f'(5) = 11f'(5)

We are given f'(5) = 7

Thus,we now have;

11 × 7 = 77

16 kids because 2 times 8 equals 16

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00