Homework 4Math 147, Fall 2017This homework is due on Thursday, September 21. Hint: If you do not have a graphingcalculator, you can use this one online: https://www.desmos.com/calculator0. Read Sections 3.2, 3.3, 3.41. For each of the following functions h(x), determine the domain and where (at whichpoints) the function is continuous. Additionally, find functions f(x) and g(x) such thath(x) = f ◦ g(x). Recall that f ◦ g(x) := f(g(x)).(a) h(x) = cosx2−31−x(b) h(x) = log3(1 − x)2. Section 1.2 # 183. Are there real numbers a and b for which the following function f (x) is continuous? Ifso, then determine a and b, and sketch a graph of f(x). If not, then explain why not.f(x) =−1 if x ≤ −1ax + b if − 1 < x < 15 if x ≥ 14. Evaluate the following limits. Show your work.(a) limx→∞−3x5+ 6x(b) limx→−∞xe−x(c) limx→∞3x3+2x5−1−x2+5(d) limx→∞x5+8−2x2+6x3(e) limx→0−cos xx(f) limx→0cos xx(g) limx→02x3cos x(h) limx→∞sin xx3+65. Section 3.2 # 8, 28, 486. Section 3.3 # 20, 287. Section 3.4 # 4, 10, 12, 168. (These problems are not to be turned in!)(a) Section 1.2 # 16(b) Section 3.2 # 5, 7, 11, 15, 20, 23, 41, 45(c) Section 3.3 # 1, 3, 5, 8, 13, 21, 25, 29(d) Section 3.4 # 2, 5, 11, 13, 15, 179. (These problems are not to be turned in!) For each function below, determine thevalue(s) (if any) of a that make f (x) continuous.(a)f(x) =(a if x ≤ πcos x if x > π(b)f(x) =(exif x < 0ax if x ≥