Question #f2dfc

1 Answer
Dec 7, 2017

See the following:

Explanation:

  1. When x tends to 2 from left, we can see that it keep vibrate. Therefore, we cannot define the limit when it tends to 2 from the left that the limit DO NOT EXIST.

  2. When x tends to 2 from right, f(x) tends to 1. Although f(2) is not exist, the limit equals to 1.

  3. lim_(x->a) f(x) exist when lim_(x->a^+) f(x)=lim_(x->a^-) f(x)
    As lim_(x->2^-) f(x) do not exist, lim_(x->2) f(x) do not exist.

  4. When x tends to 0 from left, lim_(x->0-) f(x)=-1
    When x tends to 0 from right,lim_(x->0+) f(x)=-1
    lim_(x->0^+) f(x)=lim_(x->0^-) f(x)=lim_(x->0) f(x)=-1

  5. When x=0, we cannot see a point on the graph. Therefore, it DO NOT EXIST.