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= e^u^2(1/2*x^(-1/2)) | = e^u^2(1/2*x^(-1/2)) | ||
= (e^x)/(2sqrt(x)) | = (e^x)/(2sqrt(x)) | ||
| − | |||
lim of x as x goes to inf x/f(x)= | lim of x as x goes to inf x/f(x)= | ||
lim of x as x goes to inf 1/f'(x)= | lim of x as x goes to inf 1/f'(x)= | ||
| Line 34: | Line 33: | ||
3) | 3) | ||
| − | 4) | + | 4) v= 2pi*xbar*A |
| + | v= int(a,b) of(2pi*x*(f(x)-g(x))) | ||
| + | xbar= int(a,b) of(x*(f(x)-g(x)))/A | ||
Revision as of 08:05, 25 September 2008
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Math 181 Honors Calculus
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tests solution
1)
a)
b)
2)a) f(x) = int(o,sqrtx)of e^t^2 dt
chain rule
where u = squrt x
using funamental therem of calc
f(u)= int(0,u) of e^t^2 dt
= e^u^2(1/2*x^(-1/2))
= (e^x)/(2sqrt(x))
lim of x as x goes to inf x/f(x)=
lim of x as x goes to inf 1/f'(x)=
lim of x as x goes to inf 1/(e^x/(2sqrt(x))=
lim of x as x goes to inf (2sqrt(x))/(e^x)=
lim of x as x goes to inf 1/(sqrt(x)e^x)=
0
3)
4) v= 2pi*xbar*A
v= int(a,b) of(2pi*x*(f(x)-g(x))) xbar= int(a,b) of(x*(f(x)-g(x)))/A
