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Evaluate the following limit: lim(x->0)(...

Evaluate the following limit: `lim_(x->0)(5^x-1)/(sqrt(4+x)-2)`

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`lim_(x->0)(5^x-1)/(sqrt(4+x)-2)`
`lim_(x->0)(5^x-1)/(sqrt(4+x)-2)xx (sqrt(4+x)+2)/(sqrt(4+x)+2)`
`=lim_(x->0)((5^x-1)(sqrt(4+x)+2))/((sqrt(4+x))^2-2^2)`
`=lim_(x->0)((5^x-1)(sqrt(4+x)+2))/(4+x-4)`
`=lim_(x->0)((5^x-1)(sqrt(4+x)+2))/x`
`=lim_(x->0)(5^x-1)/x xx lim_(x->0) sqrt(4+x)+2`
`=(sqrt(4+0)+2)lim_(x->0)(5^x-1)/x`
`=4lim_(x->0)(5^x-1)/x`
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