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Mattofix
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Homework Statement
i)
[tex]\int[/tex][tex]^{\infty}_{}[/tex] (cos x)/(x +exp(x)) dx
[tex]_{ 0}[/tex]
ii)
[tex]\int[/tex][tex]^{\infty}_{}[/tex] (x + [tex]\sqrt{x})^{-1}[/tex]dx
[tex]_{ 1}[/tex]
iii)
[tex]\int[/tex][tex]^{\infty}_{}[/tex] (1 + x[tex]^{3}[/tex])[tex]^{-1/2}[/tex] dx
[tex]_{ 1}[/tex]
The Attempt at a Solution
i) x +exp(x) [tex]\geq[/tex] 1-1[tex]\leq[/tex]cos x [tex]\leq[/tex]1
-1[tex]\leq[/tex](cos x)/(x +exp(x))[tex]\leq[/tex]1/(x +exp(x))
then do i have to compare something to something knowing for certain that something convereges?
For ii) + iii) please can someone nudge me in the right direction.
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