Question

lim_(x->-9) (9 - abs(x))/(9 + x)

Answer 1

I need to prove it from the right and left side.

Answer 2

since x<0 then |x|=-x

Answer 3

^that is all we need right there -9 is negative from both left and right of -9
|

Answer 4

lim x->-9 from left is 9-(-x) / (9+x) = 1
but I don't know how to do the limit from right side

Answer 5

like I said samething |x|=-x from both sides of -9

Answer 6

lim x-> -9 from right is 9-x/ (9+1) so what's the answer?? It should be 1 ( I checked my book the total limit is 1. but I don't understand the right side

Answer 7

you mean (9-(-x))/(9+x)=1 since x->-9
limit is 1 from both sides

Answer 8

that is only from left when x= -x. when it is from the right side, x= x, therefore 9-x/(9+1) , which is not equal to 1

I know the left limit is 1 -> (9-(-x))/(9+x)=1

Answer 9

right limit is the same since |x|=-x since x<0 from both sides of -9