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Question
Evaluate the following Limits: `lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/x]`
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Solution
`lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/x]`
= `lim_(x -> 0) (("a"^x - 1) + ("b"^x - 1) + ("c"^x - 1))/x`
= `lim_(x -> 0) (("a"^x - 1)/x + ("b"^x - 1)/x + ("c"^x - 1)/x)`
= `lim_(x -> 0)(("a"^x - 1)/x) + lim_(x -> 0)(("b"^x - 1)/x) + lim_(x -> 0)(("c"^x - 1)/x)`
= log a + log b + log c ...`[lim_(x -> 0) ("a"^x - 1)/x = log "a"]`
= log (abc).
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