lim x--> ?

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1 Answer
Jan 25, 2017

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#