50 POINTS! Please help ASAP

The Second Gate
As you move through the first gate, you can see another gate not far in front of you. You approach the second gate and your computer reads: "There are 2 values for which the below function does not exist. The passcode is the limit of g(x)
as x
approaches the smaller of these two values."

g(x)=x+7x2−49

Your computer also reminds you to type "infinity" for ∞
, "-infinity" for −∞
, and "NA" if the limit does not exist.

What do you enter for your computer to translate?

To find the limit of the function g(x) as x approaches the smaller of the two values for which the function does not exist, we need to determine these values first.

The function g(x) is defined as g(x) = x + 7x^2 - 49. We want to find the values of x for which the function does not exist. In other words, we need to find the values of x that make the function undefined.

The function g(x) will be undefined if the denominator of the fraction becomes zero. In this case, the denominator is x^2 - 49. To find the values of x for which the denominator becomes zero, we set it equal to zero and solve for x:

x^2 - 49 = 0

(x - 7)(x + 7) = 0

From this equation, we can see that the function will not exist when x is equal to 7 or -7.

Now that we know the values for which the function does not exist, we need to find the limit of g(x) as x approaches the smaller of these two values. In this case, the smaller value is -7.

To find the limit, we substitute -7 into the function g(x):

g(-7) = -7 + 7(-7)^2 - 49

g(-7) = -7 + 7(49) - 49

g(-7) = -7 + 343 - 49

g(-7) = 287

Therefore, the passcode to enter into your computer is 287.