Question

How do I calculate the limit of x-√x? where x is nearing to infinity

Answer 1

`lim_(x→∞)(x-sqrtx)=oo`

Explanation:

We need to find `lim_(x→∞)(x-sqrtx)=lim_(x→∞)(sqrtx(sqrtx-1))`. Using the limit laws, we can rewrite this as lim_(x→∞)sqrtx lim_(x→∞)(sqrtx-1)#.

Just by considering the graphs of these two functions, we know they increase without bound, so their limits will be infinity.

`therefore lim_(x→∞)(sqrtx(sqrt x-1))=oo`