It’s the product of three and nine.
The answers are..
6. 55
7. 6
8. 39
9. 17
The values of x at wich F(x) has local minimums are x = -2 and x = 4, and the local minimums are:
<h3>
What is a local maximum/minimum?</h3>
A local maximum is a point on the graph of the function, such that in a close vicinity it is the maximum value there. So, on an interval (a, b) a local maximum would be F(c) such that:
c ∈ (a, b)
F(c) ≥ F(x) for ∀ x ∈ [a, b]
A local minimum is kinda the same, but it must meet the condition:
c ∈ (a, b)
F(c) ≤ F(x) for ∀ x ∈ [a, b]
A) We can see two local minimums, we need to identify at which values of x do they happen.
The first local minimum happens at x = -2
The second local minimum happens at x = 4.
B) The local minimums are given by F(-2) and F(4), in this case, the local minimums are:
If you want to learn more about minimums/maximums, you can read:
brainly.com/question/2118500
Looks like the given limit is
With some simple algebra, we can rewrite
then distribute the limit over the product,
The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.
For the second limit, recall the definition of the constant, <em>e</em> :
To make our limit resemble this one more closely, make a substitution; replace 9/(<em>n</em> - 9) with 1/<em>m</em>, so that
From the relation 9<em>m</em> = <em>n</em> - 9, we see that <em>m</em> also approaches infinity as <em>n</em> approaches infinity. So, the second limit is rewritten as
Now we apply some more properties of multiplication and limits:
So, the overall limit is indeed 0:
It is a down shift of 3.
Also written as (x, y-3)
