Which expression is equivalent to sin^2x-sin x-2/sin x-2
1 answer:
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Answers:
Vertical asymptote: x = 0
Horizontal asymptote: None
Slant asymptote: (1/3)x - 4
<u>Explanation:</u>
d(x) =
=
Discontinuities: (terms that cancel out from numerator and denominator):
Nothing cancels so there are NO discontinuities.
Vertical asymptote (denominator cannot equal zero):
3x ≠ 0
<u>÷3</u> <u>÷3 </u>
x ≠ 0
So asymptote is to be drawn at x = 0
Horizontal asymptote (evaluate degree of numerator and denominator):
degree of numerator (2) > degree of denominator (1)
so there is NO horizontal asymptote but slant (oblique) must be calculated.
Slant (Oblique) Asymptote (divide numerator by denominator):
- <u>(1/3)x - 4 </u>
- 3x) x² - 12x + 20
- <u>x² </u>
- -12x
- <u>-12x </u>
- 20 (stop! because there is no "x")
So, slant asymptote is to be drawn at (1/3)x - 4
Given:
The function is
where, function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.
To find:
Number of complex and real zeros.
Time intervals for which the population increased and population deceased.
Solution:
We have,
Here, degree of function x is 3. It means, the given function has 3 zeros.
From the given graph it is clear that, the graph of function r(x) intersect x-axis at once.
So, the given function r(x) has only one real root and other two real roots are complex.
Therefore, function r has 2 complex zeros and one real zero.
Before x=6, the graph of r(x) is below the x-axis and after that the graph of r(x) is above the x-axis.
Negative values of r(x) represents the decrease in population and positive value of r(x) represents the increase in population.
Therefore, based on instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.