Answer:
Step-by-step explanation:
The owner of an ice cream shop wants to determine whether there is a relationship between ice cream sales and temperature. The o
1 answer:
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Answer:
To Prove: is equal to the sum of its Maclaurin series.
Step-by-step explanation:
If , then
for all n. If d is any positive number and |x| ≤ d, then
So Taylor's Inequality, with a = 0 and M = , says that
Notice that the same constant works for every value of n.
But, since ,
We have
It follows from the Squeeze Theorem that and therefore
for all values of x.
By this theorem above, is equal to the sum of its Maclaurin series, that is,
for all x.
Answer:
There are an absolute minimum (x = 6) and an absolute maximum (x = 12).
Step-by-step explanation:
The correct statement is described below:
Find the absolute maximum and minimum values of the function below:
,
Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.
First, we obtain the first derivative of the function and equalize it to zero:
(Eq. 1)
As we can see, only a solution is a valid critical value. That is:
Second, we determine the second derivative formula and evaluate it at the only critical point:
(Eq. 2)
x = 6
(Absolute minimum)
Third, we evaluate the function at each extreme of the given interval and the critical point as well:
x = 2
x = 6
x = 12
There are an absolute minimum (x = 6) and an absolute maximum (x = 12).