1. The problem statement, all variables and given/known data 2 problems. 1) Find an example of a function f such that : the line y=2 is a horizontal asymptote of the curve y=f(x) the curve intersects the line y=2 at the infinitive number of points 2) The position of an object moving along x axis is given at time t by: s(t)= 4t-4 if 2<t<8 and = -68 +t(20-t) if 8<=t<=10 Determine the acceleration and the velocity at any time t. Is the velocity continuous? Is acceleration continuous? 2. Relevant equations 3. The attempt at a solution For the first one, I'm really puzzled how y=2 can be horizontal asymptote, AND that the curve intersects it at infinitive points. I'm guessing that the function is y=2cos(1/x), as , y=2 is an asymptote even if my guess is right, how exactly should I solve that? For the second one, I found derivatives of s and s' s'= 4 if 2<t<8 s'= 20-2t if 8<=t<=10 s''=0 if 2<t<8 and s"= -2 if 8<=t<=10 what then? how do i check if they are continuous? I know the definition of continuous function and what exactly is horizontal asymptote, but I have no idea how to solve these two problems here :(. Help!