1) A bathtub originally contains 6 gallons of water. A faucet is turned on and continues to fill the tub at a rate of 2 gallons
1 answer:
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Answer:
3/2 < x < 2
Step-by-step explanation:
We assume the problem is ...
[tek]\dfrac{1}{x-2}<-2[/tex]
This will not be true for x-2 > 0 because that would make the left side positive. So, we must have x < 2, which makes the denominator negative. Multiplying by (x-2), we get ...
1 > -2(x -2)
1 > -2x +4
2x > 3 . . . . . . add 2x-1
x > 3/2
From above, we also have x < 2, so the solution set is ...
3/2 < x < 2
Rationalize both the numerator and denominator. Given
we can rationalize it by introducing conjugates of the numerator and denominator:
Then the limit is equivalent to
For the remaining expression, divide through uniformly by :
As <em>n</em> goes to infinity, the remaining terms containing <em>n</em> converge to 0, leaving
making the overall limit 3.