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? asked in Education & ReferenceHomework Help · 9 years ago

Limits with absolute functions?

I. lim as x approaches c of f(x)= L

II. lim as x appoaches c of abs(f(x))= abs(L)

I was asked which of the following statements are true

for all c and all L?

I thought it was both I and II, but it was wrong. I don't understand why both aren't true. Can someone explain please?

1 Answer

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  • s k
    Lv 7
    9 years ago

    With how little information is given, I'd have to say neither is true.

    Take f(x) = {1 : x ≤ 0 ; 2 : x > 0}, c = 0.

    Then there is no L such that I or II is true.

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