# Evaluating a limit

• September 23rd 2009, 09:32 PM
jzellt
Evaluating a limit
lim (x --> -8) of:

(square root(1-x)) - 3 divided by 2 + (cube root(x))

I believe I should multiply by the congugate, but I'm not getting anywhere.

Thanks for any help
• September 23rd 2009, 09:41 PM
mr fantastic
Quote:

Originally Posted by jzellt
lim (x --> -8) of:

(square root(1-x)) - 3 divided by 2 + (cube root(x))

I believe I should multiply by the congugate, but I'm not getting anywhere.

Thanks for any help

I suggest that you first make the substitution $x = t^3$:

$\lim_{t \rightarrow -2} \frac{\sqrt{1 - t^3} - 3}{2 + t}$.

Now multiply numerator and denominator by the conjugate surd, factorise the numerator, divide numerator and denominator by the common factor and then take the limit.