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what happened with -2x in 4th line?

oh i made the exponent positive by putting it in the denominator
1/x = x^-1

Is this limes 0 because e^2x goes faster to infinity that 1-2x does?

um when i went lim 1-2x = 1-infinity ??
i was substituting infinity in for x to evaluate lim

Thank you both :)

tag!!