- 117
- 8
Homework Statement:
- lim(x->-2) (x^2 +2x) /(1-abs(x+3))
Homework Equations:
- setting the limit we get 2.
but plugging -2 you clearly get a 0/0 answer. which one is correct?
is x=-2 an asymptote?
is x=-2 an asymptote?
The limit is of the form ##0/0## which is why it's non trivial to evaluate.Homework Statement: lim(x->-2) (x^2 +2x) /(1-abs(x+3))
Homework Equations: setting the limit we get 2.
but plugging 2 you clearly get a 0/0 answer. which one is correct?
is x=-2 an asymptote?
The point with limits of the form 0/0 is that you cannot just ”plug in” the value of the variable.Homework Statement: lim(x->-2) (x^2 +2x) /(1-abs(x+3))
Homework Equations: setting the limit we get 2.
but plugging -2 you clearly get a 0/0 answer. which one is correct?
is x=-2 an asymptote?
ok well what happens with the function at EXACTLY f(-2) ? limits we are tending to a point. I want to to know what happens at that exact point. surely its undefined.The point with limits of the form 0/0 is that you cannot just ”plug in” the value of the variable.
The function is undefined at that point. The limit depends only on values of the function at other points.ok well what happens with the function at EXACTLY f(-2) ? limits we are tending to a point. I want to to know what happens at that exact point. surely its undefined.
ok if its undefined at that point then surely x=-2 is an asymptote.The function is undefined at that point. The limit depends only on values of the function at other points.
Look up the definition of asymptote. That's something different.ok if its undefined at that point then surely x=-2 is an asymptote.
which the function cannot cross since its undefined at that point, ergo an asymptote. we can have horizontal, vertical and also y=kx+m asymptotes.Look up the definition of asymptote. That's something different.
##x = -2## is a vertical line.
That's not an asymptote. Look up the definition.which the function cannot cross since its undefined at that point, ergo an asymptote. we can have horizontal, vertical and also y=kx+m asymptotes.
ya forgot lim fx/x thanksThat's not an asymptote. Look up the definition.
If you've come to learn, believe me that's not an asymptote.
For this function, see if you can find the real asymptotes. There are two.
What you have is a removable discontinuity at ## x = -2##.which the function cannot cross since its undefined at that point, ergo an asymptote. we can have horizontal, vertical and also y=kx+m asymptotes.
can i say the function is undefined at x=-2?What you have is a removable discontinuity at ## x = -2##.
Yes.can i say the function is undefined at x=-2?
so how is that different from using asymptotes when figuring out where the function is defined. so the function is NOT defined at X=-2?Yes.
Yes, it's undefined at x = -2.ok well what happens with the function at EXACTLY f(-2) ? limits we are tending to a point. I want to to know what happens at that exact point. surely its undefined.
ok if its undefined at that point then surely x=-2 is an asymptote.
It's fairly obvious that the function is undefined at x = -2. The whole point of evaluating this limit is to determine whether there is a removable discontinuity at x = -2 (a "hole" in the graph) or that the function's values become unbounded (go to ##\infty## or ##-\infty## -- a vertical asymptote).can i say the function is undefined at x=-2?
The signals being sent to you are very clear.so writing the definition parameters x=-2 is undefined? well that is what i've been saying the entire time. if you read the thread im getting mixed signals here.
It's not. Why do you think it is?why is y=x-2 an asymptote
I agree that y = -x is an oblique asymptote. Does your textbook say otherwise?but y=-x is not?
the math checks out.
it says y=x-2 is and y=-x is not. is it possible y=x-2 is an asymptote for x<-3 ? and vice versa?It's not. Why do you think it is?
I agree that y = -x is an oblique asymptote. Does your textbook say otherwise?
For very large x, I get an oblique asymptote of y = -x. For very negative x, I get an oblique asymptote of y = x - 2, which agrees with what you have.it says y=x-2 is and y=-x is not. is it possible y=x-2 is an asymptote for x<-3 ? and vice versa?