Let f(x) = { |x- 3|/(x - 3), x ≠ 3, 0, x = 3 Show that lim(x→3) f(x) does not exist.

Question

Let f(x) = \(\begin{cases} \cfrac{|\text x-3|}{(\text x-3)},\quad \text x\neq3\\ 0, \quad\text x=3 \end{cases}\)

{ |x- 3|/(x - 3), x ≠ 3, 0, x = 3

Show that \(\lim\limits_{\text x \to0} \) f(x) does not exist.

Answer 1

 Let f(x) = \(\begin{cases} \cfrac{|\text x-3|}{(\text x-3)},\quad \text x\neq3\\ 0, \quad\text x=3 \end{cases}\)

{|x- 3|/(x - 3), x ≠ 3, 0, x = 3

Left Hand Limit(L.H.L.):

Right Hand Limit(R.H.L.):

Thus, \(\lim\limits_{\text x \to0} \) f(x) does not exist.