Which one or ones of the following statements is/are true?

if the line x = 1 is a vertical asymptote of y = f(x), then f is not defined at x = 1.
if f(2) > 0 and f(4) < 0, then there exists a number c between 2 and 4 such that f(c) = 0.
if f is continuous at x = 5 and f(5) = 2 and f(4) = 3, then the limit as x approaches 2 of the quantity 4 times x squared minus 11 equals 2.
a. i only

b. ii only

c. iii only

d. all statements are true.

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).