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Evaluate the limit using L'hopitals rule.

lim x->0 (6^x-11^x)/(x)

L'hopitals rule states that

if lim x->0 f(x)/g(x) yields 0/0,

then it can be re-interpreted as lim x->0 f'(x)/g'(x)

lim x->0 (6^x-11^x)/(x) clearly fits the above requirement, hence it can be rewritten as

lim x->0 [d/dx(6^x-11^x)]/d/dx(x)

= lim x->0 (ln6 * 6^x - ln11 * 11^x)/ (1)

= ln6 * 6^0 - ln11* 11^0

= ln6 - ln11

= ln (6/11) (shown)

Hope this helps. Peace.

Calculus

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