Question

Question #0404c

Answer 1

`lim_(x to oo)(1-x^3)/(2x+2)=-oo`

Explanation:

The limit is `lim_(x to oo)(1-x^3)/(2x+2)`

Here we let `x=oo` then `(1-x^3)/(2x+2)=(-oo)/(oo)=` Undefined

So therefore we can apply the L'Hospital's rule in which we differentiate the numerator and denominator individually with respect to `x`

`lim_(x to oo)(d/dx(1-x^3))/(d/dx(2x+2))`

`lim_(x to oo)(-3x^2)/2`

Now when we let `x=oo` , we get

`lim_(x to oo)(-3x^2)/2=(-3oo^2)/2`

`(-3oo^2)/2` will always equal `-oo` as `oo` is not an actual number, just a concept.

So finally, `lim_(x to oo)(1-x^3)/(2x+2)=-oo`

If you want to learn another method besides the L'Hospital's rule then PM me.