find limits

Question

find lim x --- -1   6x+5

                               _______

                                  5x-6      

 

and find lim x--- 3     x-3

                                  ________

                                    ^2-3

Answer 1

(6x + 5)/(5x - 6) is well-behaved at x = -1.

 

lim x --> -1 of (6x + 5) / (5x - 6)

 

= (6*-1 + 5) / (5*-1 - 6)

 

= -1 / -11 = 1/11

 

 

 

(x - 3) / (x² - 3) is well-behaved at x = 3.

 

lim x --> 3 of (x - 3) / (x² - 3)

 

=(3 - 3) / (3² - 3) = 0 / 6 = 0