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! (Wink)

Re: Need help limit problem

Quote:

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! (Wink)

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

Re: Need help limit problem

Quote:

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! (Wink)

Are you familiar with the definition of limit?

Re: Need help limit problem

Quote:

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.

Re: Need help limit problem

Quote:

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.