Let f(x)=2x^3-4x+1. Fill in the blank with the number of times the output value (y) occurs for input values of x between -3 and
3 (options listed in answer bank). Graph on your calculator in an appropriate window so you can count how many times.
1 answer:
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Answer:
The volume is
Step-by-step explanation:
The General Slicing Method is given by
<em>Suppose a solid object extends from x = a to x = b and the cross section of the solid perpendicular to the x-axis has an area given by a function A that is integrable on [a, b]. The volume of the solid is</em>
Because a typical cross section perpendicular to the x-axis is a square disk (according with the graph below), the area of a cross section is
The key observation is that the width is the distance between the upper bounding curve and the lower bounding curve
The width of each square is given by
This means that the area of the square cross section at the point x is
The intersection points of the two bounding curves satisfy , which has solutions x = ±1.
Therefore, the cross sections lie between x = -1 and x = 1. Integrating the cross-sectional areas, the volume of the solid is
Answer:
30
Step-by-step explanation:
The ring operator signifies a composition of functions. The composition is evaluated right-to-left. That means the composition ...
should be interpreted to mean ...
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To evaluate f(g(6)), we first evaluate g(6):
g(6) = 6² -5 = 31
Then we evaluate the function f using that as its argument:
f(31) = 31 -1 = 30
f(g(x)) = 30