Answer:
<em>9, 23, 45, 75, </em><em>113, 159</em>
Step-by-step explanation:
<u>Quadratic Sequence</u>
The difference between two consecutive terms of a quadratic sequence is another sequence, this one is an arithmetic sequence.
The first terms are given as:
9, 23, 45, 75, ...
Let's compute the differences:
23 - 9 = 14
45 - 23 = 22
75 - 45 = 30
Note the differences form an aritmetic sequence of commons difference 8.
The next two terms will be formed adding 8 to the previous difference, that is:
30 + 8 = 38 is the next difference. And the next term is
75 + 38 = 113
38 + 8 = 46 is the next difference, and the next term is
113 + 46 = 159
Thus, the complete sequence is
9, 23, 45, 75, 113, 159
33493.33
The function is continuous. [False]
Both pieces of the function are continuous, so the overall continuity of depends on continuity at .
We have
and
The one-sided limits do not match, so is not continuous at .
As approaches positive infinity, approaches positive infinity. [False]
is a large negative number when is very large, so is approaching negative infinity.
The function is decreasing over its entire domain. [True]
This requires on the entire real line. Compute the derivative of .
• for all real , so whenever .
• for all real , so and . Equality occurs only for , which does not belong to .
Whether the derivative at exists or not is actually irrelevant. The point is that if for all real .
The domain is all real numbers. [True]
There are no infinite/nonremovable discontinuities, so all good here.
The -intercept is 2. [True]
When ,