Let f be a function with domain R. Is each of the following claims true or false? If it is false, show it with a counterexample with justifications. If it is true, prove it directly from the formal definition of a limit. (a) IF lim x->infinity f(x) = 0 and f(x) never vanishes THEN lim x-> infinity cos(1/f(x)) does not exist. Please fill the blank with TRUE or FALSE.

Let f be a function with domain R. Is each of the following claims true or false? If it is false, show it with a counterexample with justifications. If it is true, prove it directly from the formal definition of a limit. 1 (a) IF lim f(x) = 0 and f(x) never vanishes THEN lim cos does not exist. Please fill the 20 -+00 x -+00 f (x ) blank with TRUE or FALSE. Final Answer This claim isIF f(0) = 0 and f(2) = 2 THEN li_>m f(cos(:1:) + 1) does not exist. Please ll the blank with TRUE or FALSE. Final Answer This claim is