To find the passcode for the second gate, we need to determine the limit of the function g(x) as x approaches the smaller of the two values for which the function does not exist. The given function is g(x) = x + 7x^2 - 49. To find the values for which the function does not exist, we need to identify the values of x that make the denominator of the function equal to zero. In this case, the denominator is 7x^2 - 49. Setting the denominator equal to zero, we have: 7x^2 - 49 = 0. Adding 49 to both sides of the equation, we get: 7x^2 = 49. Dividing both sides by 7, we have: x^2 = 7. Taking the square root of both sides, we obtain: x = ±√7. Thus, the two values for which the function does not exist are x = √7 and x = -√7. To find the passcode, we need to evaluate the limit of g(x) as x approaches the smaller of these two values. Since the smaller value is x = -√7, we substitute this value into the function: g(-√7) = -√7 + 7(-√7)^2 - 49. Simplifying this expression, we have: g(-√7) = -√7 + 7(7) - 49. g(-√7) = -√7 + 49 - 49. g(-√7) = -√7. Therefore, the passcode to enter into the computer is -√7. It's worth mentioning that if the limit did not exist, we would enter "NA" as the passcode. However, in this case, the limit exists and is equal to -√7, so we enter -√7 as the passcode
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