Basic Calculus

[Mila892]

Show that the limit of as x approaches 1 does not exist. Show the complete notation in this problem before solving and proving.

 

[khansaheb]

Show that the limit of as x approaches 1 does not exist. Show the complete notation in this problem before solving and proving.

of What?

Please show us what you have tried and exactly where you are stuck.
Please follow the rules of posting in this forum, as enunciated at:
READ BEFORE POSTING
Please share your work/thoughts about this problem

 

[Steven G]

Of course the OP means the function f(x) = |x-1|. There couldn't any other function, like f(x) = |x-1| +11 or 1/(x-1), whose limit dne as x approaches 1.

 

[khansaheb]

the OP means the function f(x) = |x-1|.

Are you registered for the mind-reading class in this semester?

 

[lookagain]

Of course the OP means the function f(x) = |x-1|.

The limit of |x - 1| as x approaches 1 exists, and it equals 0.

 

[mario99]

The limit of |x - 1| as x approaches 1 exists, and it equals 0.

I think that professor Steven mixed between the continuity and differentiability of [imath]|x - 1|[/imath] at [imath]x = 1[/imath]. Yeah, this function is continuous at [imath]x = 1[/imath] because its limit exists as [imath]x \rightarrow 1[/imath], but it isn't differentiable at [imath]x = 1[/imath].

 

[Steven G]

I think that professor Steven mixed between the continuity and differentiability of [imath]|x - 1|[/imath] at [imath]x = 1[/imath]. Yeah, this function is continuous at [imath]x = 1[/imath] because its limit exists as [imath]x \rightarrow 1[/imath], but it isn't differentiable at [imath]x = 1[/imath].

Yes, you are correct! BTW, I failed the mind reading class.

 

[mario99]

Yes, you are correct! BTW, I failed the mind reading class.

You didn't fail completely. The probability the OP meant [imath]\ \displaystyle \lim_{x\rightarrow 1}\frac{1}{x - 1} \ [/imath] is very high.

 

[khansaheb]

OP meant lim⁡x→11x−1 \ \displaystyle \lim_{x\rightarrow 1}\frac{1}{x - 1} \ x→1limx−11 is very high. (response #8 above}

How did you come you this conclusion from the Original Post?

 

[mario99]

How did you come you this conclusion from the Original Post?

I have just guessed this conclusion by comparing post #1 with post #3 written by Pro. Steven.

Note: If we don't make guesses, non of the differential equations in the world would have been solved!

 

[Dr.Peterson]

I have just guessed this conclusion by comparing post #1 with post #3 written by Pro. Steven.

Note: If we don't make guesses, non of the differential equations in the world would have been solved!

Of course, guessing what the actual problem is, is different from guessing a possible solution to a problem and checking whether it works.

On the other hand, here the "check" is whether the OP responds and says, yes, that's what it was.

And in either case, until there is some verification, we are just playing with ideas. And in both cases, the "guess" is based on experience with similar problems. So it's a stronger parallel than it initially looks!