evaluate the following limit

Question

Evaluate the following limit lim  [8−√x]/[8+√x]

                                        x→∞

Answer 1

If we plug in x=∞, we get an indeterminate.  So we can use L'Hospital Rule.  Derivative of top over derivative of bottom.

 

lim    ( -(1/2)x^-1/2) / ((1/2)x^-1/2)

x->∞

 

lim     -1

x->∞

 

 

As x approaches infinity, the value gets closer to -1.