- #1

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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