Find the limit, if it exists. lim x→−6 7x + 42 |x + 6|

Question

Find the limit, if it exists.

lim x→−6 7x + 42

|x + 6|

Answer 1

lim_x→-6 [(7x+42) / lx+6l] has the indeterminate form 0/0

If x<-6, then x+6 < 0. So, lx+6l = -(x+6)

Thus, lim_x→-6- [(7x+42) / lx+6l] = lim_x→-6- [7(x+6) / -(x+6)] = -7

On the other hand, if x>-6, then lx+6l = x+6

So, lim_x→-6+ [(7x+42) / lx+6l] = lim_x→-6+[7(x+6)/(x+6)] = 7

Since the one-sided limits are different, the limit does not exist.

Answer 2

Check it out!