Question

Find lim x->2 g(x) provided that limx-> (4-g(x)/x) =5 A) lim x→2g(x)=1

B) lim x→2g(x)=2

C) lim x→2g(x)=3

D) lim x→2g(x)=4

Answer 1

None of the provided options. Given the limit of (4 - g(x))/x as x approaches 2 is 5, solving for g(x) gives us a value of -6 when x is 2. This indicates that none of the provided answer choices are correct.

Step-by-step explanation:

The question asks us 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.

To find this limit, we can set up an equation from the given information:

lim x→2 (4 - g(x))/x = 5

We can solve for g(x) when x approaches 2:

5 = (4 - g(x))/x

5x = 4 - g(x)

g(x) = 4 - 5x

Now, let's find the value of g(x) as x approaches 2:

g(2) = 4 - 5(2)

g(2) = 4 - 10

g(2) = -6

So none of the provided options (A: 1, B: 2, C: 3, D: 4) is correct. The limit of g(x) as x approaches 2 is -6.