Which algebraic expression represents this word description?
1 answer:
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Recall that a rational function:
has a vertical asymptote at x₀ if and only if:
Also, the roots of the above rational function are the same as P(x).
Since the rational function has a vertical asymptote at x=-1, we get that its denominator must be:
Since the rational function has a double zero at x=2 we get that its numerator must be of the form:
Finally, since the rational function has y-intercept at (0,2) we get that:
Simplifying the above equation we get:
Dividing the above equation by 4 we get:
Therefore, the rational function that satisfies the given conditions is:
Answer:
The numerator is:
The denominator is:
Answer:
Infinite series equals 4/5
Step-by-step explanation:
Notice that the series can be written as a combination of two geometric series, that can be found independently:
The first one: is a geometric sequence of first term (
) "1" and common ratio (r) "
", so since the common ratio is smaller than one, we can find an answer for the infinite addition of its terms, given by:
The second one: is a geometric sequence of first term "1", and common ratio (r) "
". Again, since the common ratio is smaller than one, we can find its infinite sum:
now we simply combine the results making sure we do the indicated difference: Infinite total sum=