Question

lim x--> ?

Answer 1

See the explanation below

Explanation:

You can simplify the expression of the function noting that:

`x^2-16 = (x+4)(x-4)`

So that we have:

`{(f(x) = x-4 " if " x < 0),( f(x) = x+4 " if " x > 0):}`

We have then:

(a) `lim_(x->-4) f(x) = lim_(x->-4) (x-4) = -8`

(b) `lim_(x->0) f(x)` does not exist, since:

`lim_(x->0^-) f(x) = lim_(x->0^-) (x-4) = -4`

`lim_(x->0^+) f(x) = lim_(x->0^+) (x+4) = 4`

(c) `lim_(x->4) f(x) = lim_(x->4) (x+4) = 8`