Question

lim |x|/x as x goes to zero

Answer 1

Now when we approach zero from left |x| should be -(x) while x will be x and hence we will have -1 but when we approach from right |x| will be x resulting 1 as the limit

Answer 2

for limiting sum you usually need to manipulate the equation because you can't sub in 0 without getting an answer divided by 0 [which will equal inifinty]. therefore you need to manipulate it.
|x|/x = x/x = 1
this is just basic division where when the numerator equals denominator the result is 1

Answer 3

The limit does not exist, because as we approach 0 from the left we get a limit of -1, while approaching 0 from the right gives us a limit of +1.

Answer 4

The numerator will always be positive in this case, but the denominator will be negative for negative x values and positive for positive x values.

Answer 5

Of course! overlooked it, Guz is correct.
No matter what value of x is put in it will always equal +-1.
.'. the equation does not approach 0
.'. not a limiting sum