Evaluate the following limits. sin(4r) (a) lime-40 sin(31) (b) lime-200 VI (c) lime-+oo The z/2 (d) limz ,0 sin (e) lime-+1 (1 + In x) 1/(z-1) Let J(x) = al/ in the domain 0 0, answer each of the following, using the word NONE if appropriate. (R is a function of the variable r only, M is a constant.) (a) Evaluate lim, + 2 R(r). (b) Evaluate lily-+0% R(I). (c) State any horizontal asymptotes for R(r). Make sure that you write it as an equation of a horizontal line. (d) Find R'(r) and identify intervals of increasing and decreasing. (c) Find R"(r) and determine intervals of concavity. (f) Determine any inflection points