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Calculus

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.

lim (tan(7x))^x
x~>0

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  1. You know that lim sinu/u = 1
    so, lim tanu/u = 1 (because lim cosu = 1)

    So, lim tan(7x)/x
    = lim (tan(7x)*7)/(7x)
    = 7 lim tanu/u where u7x
    = 7

    or, using L'Hospital,

    lim tan(7x)/x
    = lim (7 sec^2(7x))/1
    = 7

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