Question

We have f(x)=x-cubicroot(x+1) Verify that f(sqrt3/9 -1) =(-2sqrt3)/9 -1 and calculate the limit of f(x) as x approaches positive infinity? Thanks!

Answer 1

See below

Explanation:

`f(x) = x- root{3}{x+1}`

`f(sqrt{3}/9-1) = sqrt{3}/9-1-root{3}{sqrt{3}/9-1+1}`
`=sqrt{3}/9-1-root{3}{{3sqrt3}/27}= sqrt{3}/9-1-sqrt{3}/3 = -{2sqrt{3}}/9-1`

Since `x` grows much faster than `root{3}{x+1}` the limit diverges, or more precisely, does not exist!