Evaluate the following limits (Give details, do not use L'Hospital's Rule, and give reasons if you think that the limit doesn't exist) 1. (a) [3 points] lim cos (sin- x) - 1 sin c (b) [3 points] lim f(x) - f(x - h) at : = 0, where f (x) = 2x - |x]. h-+0 h V5t# + 216 - 14 (c) [4 points] lim (d) [4 points] lim Vu cos(sin u + 6u - 18) Vu 2. [3 points] Let a be a constant and define f by sin (ar) if & #0. f(x) = 3c 1/6, if r = 0. For what value of a is f continuous at r = 0? Give reasons. 3. [2 points] Let f,g, h be differentiable functions defined for all values of r with values given by h(0) = 3, h'(0) = 0, h'(1) = 4, h(1) = 0, g(0) = 1, g'(0) = 2, f'(1) = 1. Ify = f(g(h(x))), find y'(1). 4. [5 points] Let y be given implicitly as a differentiable function of r by the relation 2x + 3xy-y' = 2. Find dy/dr at the point where r = 1, and y = 0. 5. [6 points] A differentiable function f with a differentiable inverse function F has the values f (1) = 0, f(2) = 1, F'(1) = 1, f'(0) = 1. Find f'(2)