(a). (5 points) Consider f(x) = tan x, for x = (-1, 1/17). Prove that f...

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(a). (5 points) Consider f(x) = tan x, for x = (-1, 1/17). Prove that f is strictly increasing. (b). (5 points) Consider its inverse, g(x): (-). Prove that = arctan x, defined as a function 9 : R 1 g'(x) = = 1+x2' xR. (c). (5 points) Prove that arctan is uniformly continuous in R. (a). (5 points) Consider f(x) = tan x, for x = (-1, 1/17). Prove that f is strictly increasing. (b). (5 points) Consider its inverse, g(x): (-). Prove that = arctan x, defined as a function 9 : R 1 g'(x) = = 1+x2' xR. (c). (5 points) Prove that arctan is uniformly continuous in R.