Here is a sample solution to 2.3 #49. Try to write your solutions in a similar style. Explainsteps if they are not obvious. You should write a solution so that another person in thecourse (who doesn’t already know how to do the problem) could read your solution andeasily understand what to do.M408c - Sample Solution2.3#49(a): Note that the numerator of g(x) factors: x2+ x − 6 = (x − 2)(x + 3). Thusg(x) = (x + 3)x − 2|x − 2|.Now,x − 2|x − 2|=1, if x > 2−1, if x < 2undefined if x = 2so we can express g(x) piece-wise asg(x) =(x + 3), if x > 2−(x + 3), if x < 2undefined if x = 2.Hence, (i):limx→2+g(x) = limx→2+(x + 3)= 5.and (ii):limx→2−g(x) = limx→2−−(x + 3)= −5.(b): The limit does not exist. Both of the one-sided limitslimx→2+g(x), and limx→2−g(x)HW 1Math 408C.exist, but they are not equal.(c):HW
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