a) Find a sequence of Lipschitz continuous functions on [0,1] whose uniform limit is x, which is a non-Lipschitz function.
b) On the other hand, show that if fn:S→R are Lipschitz with a uniform constant K (meaning all of them satisfy the definition with the same constant) and {fn}n=1∞ converges pointwise to f:S→R, then the limit f is a Lipschitz continuous function with Lipschitz constant K.