1. (1 point) Suppose f (x) = Inx. (a) Find the linear approximation of f at a = 1. L(x) = - (b) Use the linear approximation to estimate In 1.42. In 1.42 # 2. (1 point) Suppose f (x) = Vx. (a) Find the equation of the tangent line (i.e. the linear ap- proximation) to f at a = 64. y= (b) Rounding to 4 decimals, use the result in part (a) to ap- proximate: V64.4 =. 3. (1 point) Suppose N() denotes a population size at time f where the dN dt =0.07N(t). If the population size at time * = 4 is equal to 100, use a linear approximation to estimate the size of the population at time 1 = 4.1. L(4.1) = 4. (1 point) Suppose f() is the weight (in grams) of a solid sitting in a beaker of water and the solid is dissolving at a rate (in grams/minute) of f' (t) = -1f(t) (6 + f(1)). If there is 6 grams of solid at time f = 2 minutes, use a lin- car approximation to estimate the solid's weight 1 second later. Answer: grams 5. (1 point) The half-life of Radium-226 is 1590 years. If a sample contains 400 mg, how many mg will remain after 4000 years? Answer: mg