Question

Let , g(x) =∫ x if x< 1 4 if x = 12 − x^2 if 1 < x ≤ 2x − 3 if x > 2Required:Evaluate each of the following, if it exists. a. lim x→1−g(x)b. lim x→1+g(x)c. g(1)d. lim x→2−g(x)e. lim x→2+g(x)f. lim x→2 g(x)

Answer 1

To evaluate the expressions, we substitute x into g(x) and observe the values obtained for different scenarios.

Step-by-step explanation:

To evaluate the given expressions, we need to substitute the values of x into the function g(x) and observe the values obtained:

a. For lim x→1−g(x), we can substitute the value x = 1 into the different pieces of g(x) and observe that g(x) is undefined at x = 1 since it is not covered by any of the given expressions for g(x).

b. For lim x→1+g(x), we again substitute the value x = 1 into the different pieces of g(x). In this case, we find that g(x) is equal to 4.

c. To find g(1), we substitute x = 1 into the different pieces of g(x) and again find that g(1) is equal to 4.

d. For lim x→2−g(x), we substitute x = 2 into the different pieces of g(x) and find that g(x) is equal to 12.

e. For lim x→2+g(x), we substitute x = 2 into the different pieces of g(x) and again find that g(x) is equal to 12.

f. Lastly, for lim x→2 g(x), we substitute x = 2 into the different pieces of g(x) and find that g(x) is equal to 12.

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