Determine whether the function f(x) is continuous

  • Thread starter naspek
  • Start date
  • #1
181
0

Homework Statement



Given that

f(x) = { x + 1 ...................; if x < 1
........{ 2 .........................; if x = 1
........{ [4(x-1)] / (x^2 - 1) ; if x > 1

Determine whether the function f(x) is continuous at x = 1

i dont know how to start..
can someone give me an idea to start..
 

Answers and Replies

  • #2
614
0


Try finding the limit of f as x approaches 1 from the left and the right (that is, with values of x < 1 and values of x > 1)
 
  • #3
181
0


ok.. for

[tex]\lim_{x \to 1^{-}} f(x)[/tex]

i got 0

for

[tex]\lim_{x \to 1^{+}} f(x)[/tex]

i got 2

am i got it right?
so.. how can i conclude it?
 
  • #4
67
0


ok so now you have to go back to the calc one definition of continuity. the requirements were
If f is continuous at a then, these 3 facts have to hold
[tex] \lim_{x \to a^{-}} f(x) = f(a) [/tex]
[tex] \lim_{x \to a^{+}} f(x) = f(a) [/tex]
[tex] \lim_{x \to a} f(x) = f(a) [/tex]
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,833
956


ok.. for

[tex]\lim_{x \to 1^{-}} f(x)[/tex]

i got 0
For x< 0, f(x)= 1+ x. Are you saying that [itex]\lim_{x\to 0} 1+ x= 0[/itex]?

for

[tex]\lim_{x \to 1^{+}} f(x)[/tex]

i got 2

am i got it right?
so.. how can i conclude it?
This function is continuous at x=0 only if the limit there exists and is equal to f(0). The limit itself exist only if those two one sided limits are the same.
 

Related Threads on Determine whether the function f(x) is continuous

Replies
2
Views
1K
Replies
3
Views
1K
Replies
4
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
9
Views
809
Replies
8
Views
1K
Replies
5
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
11
Views
620
Replies
6
Views
1K
Top