- #1
SirPlus
- 18
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1. Homework Statement [/b]
Use the direct comparison test to show that the following are convergent:
(a)[itex]\int_1^∞[/itex] [itex]\frac{cos x\,dx}{x^2}[/itex]
I don't know how to choose a smaller function that converges similar to the one above. The main problem is i don't know where to start.
A simple one that i could solve is : (b)[itex]\int_0^∞[/itex] [itex] \frac{1\,dx}{e^x + 1}[/itex] where a similar function(yet greater) is --> (c)[itex]\int_0^∞[/itex][itex] \frac{1\,dx}{e^x}[/itex] that converges to 1.
Problem :
If cosines and logs come into the integral - i get confused. What do i do?
Use the direct comparison test to show that the following are convergent:
(a)[itex]\int_1^∞[/itex] [itex]\frac{cos x\,dx}{x^2}[/itex]
I don't know how to choose a smaller function that converges similar to the one above. The main problem is i don't know where to start.
A simple one that i could solve is : (b)[itex]\int_0^∞[/itex] [itex] \frac{1\,dx}{e^x + 1}[/itex] where a similar function(yet greater) is --> (c)[itex]\int_0^∞[/itex][itex] \frac{1\,dx}{e^x}[/itex] that converges to 1.
Problem :
If cosines and logs come into the integral - i get confused. What do i do?
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