Question 10 is not necessary to do but if you can I'll appreciate it. Can we please show all steps thank you

(17 points) 8. Let if x 5 Evaluate the limits listed below. If a limit does not exist explain why. a lim f (x) X-+0 b. lim f (x) x-$0' c. lim f (x) X-5 d lim f (x) e lim f (x) X-5 f lim f(x) X-XD g- lim f (x) X -0 Where is the function not continuous? Explain. 9 points) 9. Give the graph of one and only one function which satisfies all the following conditions. a Domain of the function [-5, 0) U (0, co) b. The function is continuous on its domain c. f (-5) = f (5) d. lim f (x) - 6 lim f(x) - 0 lim f (x) = 0 lim f (x) = -co Explain why the graph of a function which satisfies all these conditions must intercept the x-axis, meaning that there is at least one number c so that f ( c) = 0. Bonus. (10 points) 10. Prove each of the statements below using the formal definition of limits. a. If lim f (x) = -co and c > 0, then lim c f (x) - -co b. If lim g(x) = co and g(x) a, then lim f (x) - co