1. (3 marks) Evaluate the limit lim f(x) = V2e2x + 1 3ex - 5 2. (4 marks) For a particular function g, we know g'(8) = 4 and g(8) = -5. Write an equation for the tangent to g at x = 8. 3. (3 marks) Determine whether the derivative of the following function exists at x = 0. f (I ) =1 0 x2 sin(1/x) if x # 0 if x = 0 Justify your answer using the definition of the derivative