When you multiply 2/3 by a fraction less than one,how does the product compare to the factors?
1 answer:
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Answer:
The general limit exists at <em>x</em> = 9 and is equal to 300.
Step-by-step explanation:
We want to find the general limit of the function:
By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.
So, let's find each one-sided limit: the left-hand side and the right-hand side.
The left-hand limit is given by:
<h3>Since the given function is a polynomial, we can use direct substitution. This yields:
Evaluate:
Therefore:
The right-hand limit is given by:
Again, since the function is a polynomial, we can use direct substitution. This yields:
Evaluate:
Therefore:
Thus, we can see that:
Since the two-sided limits exist and are equivalent, the general limit of the function does exist at <em>x</em> = 9 and is equal to 300.
The 2-point form of the equation of a line is
.. y = (y2 -y1)/(x2 -x1)*(x -x1) +y1
For your points (x1, y1) = (0, 3) and (x2, y2) = (3, 5), this is
.. y = (5 -3)/(3 -0)*(x -0) +3
.. y = (2/3)x +3
Written as a function, it is
.. f(x) = (2/3)x +3
.. y = (y2 -y1)/(x2 -x1)*(x -x1) +y1
For your points (x1, y1) = (0, 3) and (x2, y2) = (3, 5), this is
.. y = (5 -3)/(3 -0)*(x -0) +3
.. y = (2/3)x +3
Written as a function, it is
.. f(x) = (2/3)x +3