Give an example of a continuous, smooth (first-order differentiable), real function f(n): RH R which satisfies the following two constraints: (1) f(n) is non-zero and positive for all real numbers n E R, and (2) f(n) is neither O(1) nor 12(1). Then, give a rigorous proof that your function f(n) is not 0(1). Finally, give a rigorous proof that your function f(n) is not 1(1). (Note: bonus credit will only be given for completely correct solutions.) Give an example of a continuous, smooth (first-order differentiable), real function f(n): RH R which satisfies the following two constraints: (1) f(n) is non-zero and positive for all real numbers n E R, and (2) f(n) is neither O(1) nor 12(1). Then, give a rigorous proof that your function f(n) is not 0(1). Finally, give a rigorous proof that your function f(n) is not 1(1). (Note: bonus credit will only be given for completely correct solutions.)