Question

i need help with calculus.
find the limit as x approaches 1 . x-1/|x-1|

Answer 1

OKay Limit doesn't exist as we approach from left we get minus inside the modulus making it -(x-1) and when we approach from right we have + inside mod x+1 so limit is 1 and -1 ..hence limit doesn't exist

Answer 2

okay this makes sense, but how could you show work? do you plug in 1?

Answer 3

myininaya is here she is better at explaining

Answer 4

satellite is suppose to make is pretty piecewise function but hes not coming :(
so i guess i will explain without his pretty piecewise function

Answer 5

hmm you just put number greater than 1 a little greater than 1 when you approach from right side and a little smaller when you approach from left side hmm you can check khan academy they have some pretty nice videos

Answer 6

\[x-1>0=> |x-1|=x-1; x-1<0=> |x-1|=-(x-1)\]

Answer 7

\[\lim_{x \rightarrow 1^+}f(x)=\lim_{x \rightarrow 1^+}\frac{x-1}{x-1}=1\]
\[\lim_{x \rightarrow 1^{-}}f(x)=\lim_{x \rightarrow 1^-}\frac{x-1}{-(x-1)}=-1\]

Answer 8

By definition of absolute value when you approach from the right you have\[y=\frac{x-1}{x-1}\]since the abs value is positive, but when you approach from the left you have\[y=\frac{x-1}{-(x-1)}\]

Answer 9

but \[1 \neq -1 \]

Answer 10

so actual limit does not exist

Answer 11

thank you so much the illustrations made it better