Question

4. Compute the following limits or state that they do not exist.
lim (|x|/x)
x->0

Answer 1

lim |x|/x

x→0

» When |x| is redefined, it opens as:

• -x , when x < 0
• x , when x > 0

» Thus;

Left Hand Limit:

lim -x/x = -1

x→0

Right Hand Limit:

lim x/x = 1

x→0

Since, Left Hand Limit ≠ Right Hand Limit, LIMIT DOES NOT EXIST FOR x→0