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SolutionLimitProbWithExplanation

# SolutionLimitProbWithExplanation - 7x 2 x 5x The following...

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Find the following limit: lim x →∞ 1 + 2 5 x 7 x The following uses the natural log function, L’Hopital’s Rule, and no ”tricks”. Let y = lim x →∞ 1 + 2 5 x 7 x Now use the properties of the natural log function to write the exponential expression as a product. Remember, the natural log function is continuous on (0 , ) . ln y = ln lim x →∞ 1 + 2 5 x 7 x = lim x →∞ ln 1 + 2 5 x 7 x = lim x →∞ 7 x ln 1 + 2 5 x We can write our product as a quotient by dividing by 1 7 x instead of multiplying by 7 x . ln y = lim x →∞ 7 x ln 1 + 2 5 x = lim x →∞ ln 1 + 2 5 x 1 7 x Now we have a quotient, so we can see if we can use L’Hopital’s Rule. This is a ” 0 0 ” form (remember, ln(1) = 0) so we can use L’Hopital’s Rule.
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