# Thread: continuity question check

1. ## continuity question check

Consider the following graph of a function F

F(x) =

1/x --> x < -1
2 --> -1 (less than or equal to) x < 1
3 --> x = 1
x+1 --> 1 < x (less than or equal to) 2
-1/(x-2) --> 2 < x

(a) Find lim x-->1- F(X)
(b) Find lim x-->-1+ F(X)
(c) Find lim x-->-1 F(X)
(d) Find lim x-->1 F(X)
(e) Is F continuous at x=1

this is what i got for the answers

(a) 1/x
(b) 2
(c) 2
(d) none
(e) no

are these answer correct?

2. Originally Posted by break
Consider the following graph of a function F

F(x) =

1/x --> x < -1
2 --> -1 (less than or equal to) x < 1
3 --> x = 1
x+1 --> 1 < x (less than or equal to) 2
-1/(x-2) --> 2 < x

(a) Find lim x-->1- F(X)
(b) Find lim x-->-1+ F(X)
(c) Find lim x-->-1 F(X)
(d) Find lim x-->1 F(X)
(e) Is F continuous at x=1

this is what i got for the answers

(a) 1/x
(b) 2
(c) 2
(d) none
(e) no

are these answer correct?

No. for (a) you have lim 2 when x --> 1- since F(x) = 2 for -1 x < 1.
(b) is right. (c) is "doesn't exist", since lim F(x) when x --> -1- doesn't equal lim F(x) = -1+: the former is 1/-1 = -1, whereas the latter is 2.
Also (d) is incorrect: the limit exists since both one-sided limits equal 2. That none of these equals F(1) only means F(x) isn't continuous at x = 1, but still the limit exists.
(e) is correct but for the reasons above, not for what you thought.

Tonio

3. oops had a typo

(a) is supposed to be

(a) Find lim x-->-1- F(X)

and also is (d) 3?

4. Originally Posted by break
oops had a typo

(a) is supposed to be

(a) Find lim x-->-1- F(X)

and also is (d) 3?

(a) Then even worse: the limit doesn't exist.

The answer for (d) and its reason I wrote in my past message

Tonio