My goal is to deeply understand these problems. So, please show me the entire process of solving these.

1) Let f be a piecewise-defined function given by: In(6 - x) +3V/5 7 + cos( 1X2) if x 5 V5 (x - 5) a) (3 points) Evaluate lim f(x). b) (3 points) Evaluate lim f(x). * +5- c) (2 points) Evaluate lim f(x). Explain where this value came from. d) (2 points) The definition of continuity is given in the "What is a limit" section of the textbook. Is the function f continuous at x = 5? Explain your answer using that definition.2) The graph of a function g(x) with domain (-4, 4) is given in the figure. This portions of this graph in the intervals (-2,0) and (2, 4) are straight lines. The portion on the interval (0, 2) is not parabolic. For each of the limits below, give the form of the limit, then evaluate the limit. Show your work and justify your answer. g(x) + sin (x) a) (3 points) lim xvx +4 FORM : VALUE : b) (3 points) im (x) + 21' FORM : VALUE : c) (4 points) lim (x2 + 2x - 15) * +3 x+ g(x) -3 FORM : VALUE :3) (10 points) Sketch a possible graph of a function satisfying all of the following properties: . f is an odd function with domain [-6, 6] . f has intervals of continuity: [-6, -4), (-4, -2]. (-2, 2), [2, 4), and (4, 6]. . f(0) = 0, f(2) = 4, and f(6) = 1 lim f (x) =2 x -+2 lim f(x) = -co and lim f(x) = co *-+4- *-+4+ . f(x) > 0 for x in (0, 3) U [4, 6] and f(x)