Consider the limit L = lim x0 (cos x) ^(1/x^2)

a) Use a calculator and some small values of x to approximate L to four decimal places.

b) Find L.

Hint: First evaluate ln(L). You may write (Form: 0/0) or

(Form: / ) to indicate an indeterminate form that is suitable for L'Hopital's theorem. You may write H to indicate an

=

equalityarising from L'Hopital's theorem.