The limit of x to the xth power ... to the xth power as x tends to zero

An inductive method simplifies the application of L'Hopital's rule to problems involving a tower of exponents, giving a limit of x to the xth power ... to the xth power as x tends to zero from the right. The expression tends to zero for odd number of x and tends to one for even number of x. The n-th hyperpower of x is evaluated using parentheses nesting and standard calculus principles. A theorem for determining the limits of x raised to a tower of exponents is presented and an inductive proof is considered.