Question

Find limx→2g(x),provided that limx→2[4−g(x)x]= 5.

Answer 1

The limit of g(x) as x approaches 2 is found to be -6 by manipulating the given limit involving g(x).

Step-by-step explanation:

We need to find the limit of g(x) as x approaches 2, given that the limit of (4 - g(x))/x as x approaches 2 is 5. Since we're given the behavior of a fraction involving g(x), we can rearrange this information to solve for the limit of g(x). To isolate g(x), we multiply both sides by x and then take the limit as x approaches 2:

limit as x approaches 2 of [4 - g(x)] = 5 * x

4 - (limit as x approaches 2 of g(x)) = 5 * 2

4 - (limit as x approaches 2 of g(x)) = 10

limit as x approaches 2 of g(x) = 4 - 10 = -6

Thus, the limit of g(x) as x approaches 2 is -6.