a) evaluate limx->infinity f(x)

b) determine whether integral converges or not

c) find the taylor polynomial

ac x2+1 F($)= K m) dt. (a) (4 Points) Evaluate lim f(:c). m>+oo 2. (18 Points) Let f(x) = (3 cos:c + (30\") and (b) (4 Points) Determine whether f f (:5) d3: converges or not. 0 (c) (10 Points) Given that f'($) e'\"C (1 :c7;2 :c3) + (3562 + (m2 +1):I:sina:+(x2 1)cos:v+3) (3132+1)2 f"(:c) : W (3132+1)3 Find the quadratic Taylor polynomial of F at the reference point 0 and use it to approximate F (0.1). In addition, derive an upper bound for the absolute error committed