Determine whether each of the following functions is continuous at 2. Name any results or rules that you use. You may use the basic continuous functions listed in Theorem D51 from Unit D4. 2-3x+x2, x 2, (i) f(x)= 2-3, (ii) f(x)= (iii) f(x)= x> 2. ((x-2) sin (2) [sin(x), x 2, 2-4, >2. The polynomial p is given by P(x)=3x-3x - 3x + 1. x2, x=2. (i) Determine a real number M such that p has no zeros outside the interval (-M, M), and exactly three zeros in (-M, M). (ii) Determine an open interval of length in R that contains exactly one zero of p. Theorem D51 Basic continuous functions The following functions are continuous: (a) polynomials and rational functions (b) f(x) = |x| (c) f(x)=x (d) the trigonometric functions sine, cosine and tangent (e) the exponential function.