Lt(x rarr0)(5^(x)-1)/(sqrt(1+x)-1)=...

`Lt_(x rarr0)(5^(x)-1)/(sqrt(1+x)-1)=`

Lt(x rarr0)(5^(x)-1)/(sqrt(1+x)-1)=
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Lt(x->0)((15)^x-5^x-3^x+1)/(1-cos4x)=
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Lt(x rarr0)(cos x+sin x)^((1)/(x))=
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Lt(x rarr0)(tan^(-1)x)/(x)
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Lt(x rarr0)(sqrt(4+x)-(8+3x)^((1)/(3)))/(x)=
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lim(x rarr 0) (sqrt(1+x)-1)/(x)=
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lim(x rarr0)sqrt(1-sqrt(1-x^(2)))
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Lt(x rarr 0)((1-2cosx+cos2x)/x^(2))
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Lt(x rarr 0)((1-2cosx+cos2x)/x^(2))
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