Thread: Left and right hand limits of a hybrid function.

Hi, I need help on this one problem: ( I can't type in the format the problem is given, so hopefully it'll be understandable.)
The question states:

Evaluate or determine that the limit does not exist for each of the limits (a) lim x--> d- f(x), (b) lim x-->d+ f(x)

f(x)={ 1/(x+1), for x>-1
x^2-3x, for x<=(less than and equal) -1

d=-1


I think the answer for (a) is 4, and (b) is 4 also, but there are no answer choices (this is multiple choice) for that. The closest is (a) 4, (b) does not exist. I don't understand why (b) is does not exist.

The answer choices are:

1) (a) does not exist
(b) 4

and

2) (a) 4
(b)Does not exist.


Any help would be appreciated, thanks!

Originally Posted by mugenkb2

Hi, I need help on this one problem: ( I can't type in the format the problem is given, so hopefully it'll be understandable.)
The question states:

Evaluate or determine that the limit does not exist for each of the limits (a) lim x--> d- f(x), (b) lim x-->d+ f(x)

f(x)={ 1/(x+1), for x>-1
x^2-3x, for x<=(less than and equal) -1


Any help would be appreciated, thanks!

I suppose the value of d is -1 ....?

Originally Posted by mugenkb2

Hi, I need help on this one problem: ( I can't type in the format the problem is given, so hopefully it'll be understandable.)
The question states:

Evaluate or determine that the limit does not exist for each of the limits (a) lim x--> d- f(x), (b) lim x-->d+ f(x)

f(x)={ 1/(x+1), for x>-1
x^2-3x, for x<=(less than and equal) -1


Any help would be appreciated, thanks!

Are you familiar with the definition of limit?

Originally Posted by mr fantastic

I suppose the value of d is -1 ....?

oh right, I forgot about that, yes, d=-1.


I think the answer for (a) is 4, and (b) is 4 also, but there are no answer choices (this is multiple choice) for that. The closest is (a) 4, (b) does not exist. I don't understand why (b) is does not exist.

The answer choices are (should have put them up in the first post) are:

1) (a) does not exist
(b) 4

and

2) (a) 4
(b)Does not exist.

Originally Posted by mugenkb2

oh right, I forgot about that, yes, d=-1.


I think the answer for (a) is 4, and (b) is 4 also, but there are no answer choices (this is multiple choice) for that. The closest is (a) 4, (b) does not exist. I don't understand why (b) is does not exist.

The answer choices are (should have put them up in the first post) are:

1) (a) does not exist
(b) 4

and

2) (a) 4
(b)Does not exist.

Option 2) is correct.

If x --> -1+ then x > -1. Look at the rule for x > -1 and consider what happens in the limit.