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Using L’Hospital Rule, Evaluate: Lim X → 0 8 X − 4 X 4 X - Mathematics

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Sum

Using L’Hospital Rule, evaluate: `lim_(x->0)  (8^x - 4^x)/(4x
)`

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Solution

`lim_(x-.0) (8^x-4^x)`
`lim_(x->0)(8^xlog8 - 4^x log 4)`

`= (8^0 log 8 - 4^0 log 4)/4`
`=1/4log2`

Concept: Definite Integral as the Limit of a Sum
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