How to solve y=3(0)^2-6(0)-5
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Answer:
all real numbers
Step-by-step explanation:
As the graph goes up, it keeps going up and to the right. There is nothing telling us it will stop moving to the right at a certain point. It goes up much faster than it goes right, but it keeps going right and up forever. That makes the domain reach positive infinity. The same happens on the left side. As it goes down to the left, it keeps going left forever to negative infinity. That makes the domain all real numbers from negative infinity to positive infinity.
Domain: all real numbers
The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.
Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is
π (radius) (height) = π (1/y)² ∆y = π/y² ∆y
and the volume of a stack of n such disks is
where is a point sampled from the interval [1, 5].
As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,
