How Does f(x) Behave as x Approaches 4 from Both Sides?

[kendal12]

Ok, so here's the the problem:

"Use a graphing calculator to sketch the following function. Find the value c where the function fails to exist, and graphically find the limit of f(x) as x approaches c from the left and the right.

f(x)= 3/(x-4)

Ok, so what I don't understand is how I can define a limit from the left and right when the function in unbounded. I know that at 4 c fails to exist, so isn't that the limit from both sides?

 

[whozum]

It says to graphically show that.

 

[kendal12]

Yeah, then it gives me a blank graph to draw the hyperbola, but then at the bottom it has:

lim f(x)=
x-->c-
and

lim f(x)=
x-->c+

What should I put here?

 

[quasar987]

What does f(x) seems to go to when x approaches 4 from the left? i.e. when x succesively takes the values 3.9, 3.99, 3.999, ...?

Then do the same thing for the limit from the right. What does f(x) seems to go to when x approaches 4 from the right? i.e. when x succesively takes the values 4.1, 4.01, 4.001 ...?

 

[kendal12]

it seems to go to infinity and negative infinity... is that what they're looking for? it seems too obvious

 

[quasar987]

It's the opposite actually: negative infinity from the left and positive infinity from the right.

This is what "find the limit graphically" means. It means "what does the limit seems to be judging by the graph?".

 

[francisco]

"Use a graphing calculator to sketch the following function. Find the value c where the function fails to exist, and graphically find the limit of f(x) as x approaches c from the left and the right.

f(x)= 3/(x-4)

the function fails to exist at 4 (c = 4). why? what happens to the graph, in other words, what are the values of f(x), as x gets closer and closer to (approaches) 4 from the left? for example, what are the values of f(x) when the values of x are 3.5, 3.8, 3.9, 3.95, 3.99, 3.995, 3.999,...and so on? as a limit, the values of x will get closer and closer to 4, but it will never reach 4. and as a limit, the values of f(x) keeps going in the negative direction of the y-axis. what is important to understand about limits is that the x values never reach the value that it is approaching. consequently, y = f(x) never reaches its corresponding value. think of a limit as a value that it is not possible, but if it would have been possible, that would have been the value. for example, it is not possible for x to reach 4, but if it would have been possible, x would have been 4, and f(x) would have been negative infinity.

this is the notation (how it is written):

lim_{x→4}f(x)=-∞

in other words, the limit of f(x) as x approaches 4 is equal to negative infinity.

you do the other half. what happens to the graph as x gets closer and closer to 4 from the right?