Testing the Continuity of k(x) at x=3: Is lim x->3- k(x) = lim x->3+ k(x) true?

[chukie]

k(x) is a continuous function. k(x)=-1 and k(4)=2 then is this statement true:

lim x->3- k(x) = lim x->3+ k(x)


i realli hv no idea. could sumone help me please?

 

[Dick]

What does continuous mean in terms of limits? k(x)=(-1) means the function is constant. k(4)=2 contradicts the previous statement. What's the real problem?

 

[chukie]

What does continuous mean in terms of limits? k(x)=(-1) means the function is constant. k(4)=2 contradicts the previous statement. What's the real problem?

sorry i typed the question wrong k(3)=-1

 

[Dick]

sorry i typed the question wrong k(3)=-1

S'ok. But the question is still odd, because the values of the function don't have anything to do with whether the two limits are equal. If a function is continuous at x=3, what can you say about it's left and right hand limits? Do you mean to say k(x) is only defined on the interval [3,4]? Or is it defined and continuous everywhere?

 

[chukie]

S'ok. But the question is still odd, because the values of the function don't have anything to do with whether the two limits are equal. If a function is continuous at x=3, what can you say about it's left and right hand limits? Do you mean to say k(x) is only defined on the interval [3,4]? Or is it defined and continuous everywhere?

k(x) is continuous for all real numbers

 

[Dick]

Fine. Then the values of the function have nothing to do with the problem. What does being continuous tell you about limits?

 

[chukie]

umm I am not exactly sure but the left hand limit should equal the right hand limit?

 

[Dick]

Pretty much. And they both should equal the value of the function at x=3. Kind of a silly question then, yes?

 

[chukie]

yes lol but thank you so much for ur help. it helped cleared things up for me.