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19.02.2021 •
Mathematics
Determine whether the following statements are true and give an explanation or counterexample. If f is not one-to-one on the interval [a, b], then the are of the surface generated when the graph of f on [a, b] is revolved about the x-axis is not defined.
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Ответ:
Step-by-step explanation:
The missing equation is:
Suppose f = nonnegative function whose first derivative is within (a,b) and it is continuous, Then the area of the surface generated is revolved about the x-axis:
The area of the surface revolution is:
So; if
for ![y \ \varepsilon \ [c,d]](/tpl/images/1130/7138/b0073.png)
Then; substituting a with c and b with d; f(x) also with g(y) and dx with dy;
Then;
SInce;
Provided that the semicircle
isn't on
interval.
Then, the solid generated by the revolution about the x-axis is a sphere.
However, the surface is well defined and the statement is false.
Ответ: