Question

How do you find the limit `(x+x^-1)/(1+sqrt(1-x))` as `x->-oo`?

Answer 1

`-oo`

Explanation:

`= lim_{x->-oo} ((x+1/x)/(1+sqrt(1-x)))*(1-sqrt(1-x))/(1-sqrt(1-x))`
`= lim_{x->-oo} (x+1/x)(1-sqrt(1-x))/x`

`"Now divide numerator and denominator by x :"`

`= lim_{x->-oo} (1+1/x^2)(1-sqrt(1-x))`

`= 1 * -oo = -oo`