2x, x>4 x=4 find lim f(x) if it exists. x-4 x-8, x <4 Given f(x)=5, Determine if the following are continuous. If the

2x, x>4 x=4 " find lim f(x) if it exists. x-4 x-8, x 3 For what value of A and B would f(x) be differentiable everywhere? Given: x-xy+y=37; dy (i) Find dx (ii) Find the equation of the tangent line to the curve at (3,2). (Show work; hint: you need to use implicit differentiation!) Suppose we are given the data in the table about the functions and g and their derivatives. Find the following values. (No work needed; write the answers only.) x 1 2 3 4 f(x) 3 2 1 4 f'(x) 1 4 2 3 g(x) 2 1 4 3 g'(x) 4 2 3 1 (a) if h(x) = f(g(x)), then h(4) = (b) if h(x) = f(g(x)), then h'(4) = (c) if k(x) = g(f(x)), then k'(4) = (d) if h(x)=- g(x) f(x)' then h'(4) = (e) if h(x) = f(x)g(x), then h'(4) =