Answer:
46.375
Step-by-step explanation:
Given information:
where, 0 ≤ x ≤ 3.
We need to divde the interval [0,3] in 6 equal parts.
The length of each sub interval is
Right end points are 0.5, 1, 1.5, 2, 2.5, 3.
The value function on each right end point are
Riemann sum:
Therefore, the Riemann sum with n = 6 is 46.375.
The exponential growth is:
And its graph is the first one.
The exponential decay is:
And its graph is the second one.
<h3>How to identify the exponential equations?</h3>
The general exponential equation is of the form:
Where A is the initial value and b is the base.
Here the two functions are:
As you can see, the base for the first one is smaller than 1, then it is an exponential decay (and it has a decreasing graph, so the graph of this one is the second graph).
For the second function, we have the base b = 1.25, which is larger than 1, so it is an exponential growth, and its graph is an increasing graph, which is the first one.
If you want to learn more about exponential functions:
#SPJ1
Given:
Consider the completer question is "Find the derivative for
."
To find:
The derivative .
Solution:
Chain rule:
Quotient rule:
We have,
Differentiate with respect to x.
Using chain rule and quotient rule, we get
Therefore, the required answer is .