Evaluate
1 answer:
A piece-wise function combines more than one functions of different input values.
<em>The value of f(-1) is -3</em>
From the graph, we have the following observations
- <em>When x = -1, y = -3</em>
- <em>When x = -1, y = -4</em>
Notice that there is a closed circle at the point where x = -1 and y = -3.
This means that y = -3 is inclusive of the values of y on that particular function
However, there is an open circle at the point where x = -1 and y = -3.
This means that y = -4 is exclusive of the values of y on that particular function
The correct corresponding value of y is when y is inclusive.
Hence, the value of f(-1) is -3
See attachment for the graph of the piece-wise functions
Read more about piece-wise functions at:
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Answer:
Step-by-step explanation:
Recall that the ratio test is stated as follows:
Given a series of the form
If L<1, then the series converge absolutely, if L>1, then the series diverge. If L fails to exist or L=1, then the test is inconclusive.
Consider the given series . In this case,
, so , consider the limit
Since the numerator has a greater exponent than the numerator, the limit is infinity, which is greater than one, hence, the series diverge by the ratio test