2. A list of the limit laws is below. For each step, state the limit law that justifies the step. Limit Laws Let f (x) and g (x) be defined for all x # a over some open interval containing a. Assume that L and M are real numbers such that lim f (x) = L and lim g (x) = M. Let c be a constant. Then, x-a x - a each of the following statements holds: Sum law for limits: lim (f (x) + g(x)) = limf(x) + limg(x) = L + M x - a Difference law for limits: lim (f (x) - g(x)) = limf(x) - limg(x) = L -M x -a Constant multiple law for limits: lim of (x) = c . lim f (x) = CL x -a x - a Product law for limits: lim (f (x) . g(x) ) = limf(x) . limg(x) = L . M x -a x - a Quotient law for limits: lim f ( x ) xim f ( x ) x-ag (x ) jim g(x ) for M + 0 Power law for limits: lim (f (x))" = lim f (x ) = Ln for every positive integer n. x- a Root law for limits: lim f (x) = " limf (x) = "VL for all L if n is odd and for L 2 0 if n is even x - a x-a and f (x) 2 0. [15 pt] A. Suppose that lim f (x) = 1 and lim g(x) = -3. Step Reasoning 2f(x) - 3g(x) lim2f (x) - 39(x) lim x -0 (f (x ) + 3) 1/2 lim (f (x) + 3)1/2 2limf (x) - 3limg(x) him (f (x) + 3) 1/2 2limf (x) - 3limg(x) lim (f ( x ) + 3 ) 2limf(x) - 3limg(x) limf (x) + lim3 )1/2 * - 0 2+ 9 ( 1+ 3) 1/2 Substitution of given values of limits