P1. Limits. a) Find the limits: 3x Vx + 4- 2 lim lim x-70./x + 8 x-0 Xb) Using the limit definition of continuity, determine whether or not the function is continuous at x = 1. x21 f(x)= whenxqtl 0 when x: 1 P2. (5 pts) Find the equation of the tangent line at x = 1 for the function g(x) = 1/; P3. Calculate the derivatives of the functions listed below using any techniques that you consider convenient. 36' a) y(t) = 8t2 + ? + 61n (t) b) 110:) = em (5) k(x) : tin (X) d) g(x) 2x31l7X 'l' 2 e) f(x) = ( + 3) (x2 + x) P5. Use the graph of f(x) below to determine the following: ro -3 -2 a) lim = d) f(3) = X-0 b) lim = e) lim = X- - 3 x-4+ c) lim = f) f(0) = x-3P6. For some painkillers the dose, D, given depends on the weight of the patient, W. Thus, D =f(W) where D is in milligrams and W is in pounds. a. Interpret the statementsl40) = 120 andf'(140) = 3 in terms of this painkiller. b. Use the information from part a to estimate145). Explain how you came to your estimate