Exercise 2: Hard] Let f,g be functions such that limc f(x) = L and lim,c g(x) = L (a) Let h(x) max{f(x),g(x)}, and let k(x) min{f(x), g(x)}. Prove that limc h(x lim ck() L. = L and (b) Define a new...

Extracted text: Exercise 2: Hard] Let f,g be functions such that limc f(x) = L and lim,c g(x) = L (a) Let h(x) max{f(x),g(x)}, and let k(x) min{f(x), g(x)}. Prove that limc h(x lim ck() L. = L and (b) Define a new function: тЕО l(x) = \g(x), otherwise. Prove that limcl(x) = L. Hint: Use part (a) and the squeeze theorem. (c) Conclude that for the function: хеQ 0, otherwise F(x) = we have lim+0 F(x) = 0.