[15 pt] 4. A list of the limit laws is below. For each step, state the...

 

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[15 pt] 4. 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 and Mare real numbers such that limf(x) = L and limg(x) = M. Let c be a constant. Then, each of the following statements holds: Sum law for limits: lim (f(x) + g(x)) = limf(x) + limg(x)=L+M Difference law for limits: lim (f(x)-g(x)) = limf(x) - limg(x)=L-M Constant multiple law for limits: lim cf(x) = c-limf(x) = cl you - Product law for limits: lim (f(x) g(x)) - limf(x) limg(x)=L-M THE Quotient law for limits: lim : A 100 x(x) Power law for limits lim ((x))" - (lim(x))" =L" for every positive integer n 1-0 Root law for limits: lim √(x) = limf(x) = VL for all L if n is odd and for L 20 if n is even and f(x) > 0. 2f(x)-3g(x) lim x-0 (f(x) + 3)¹/2 Suppose that limf(x) = 1 and lim g(x) = -3. Step lim, foxx) lim2f(x)-3g(x) lim(/(x) + 3)1/² 2limf(x) - 3limg(x) lim(f(x) + 3)¹/2 X40 2limf(x) - 3limg(x) 1/2 lim(f(x) + 3) -31img(x) 2limf(x) - 1/2 (limf(x) + lim3)" 2+9 11 2 (1+3)¹/2 THE = for M0 stitutio Reasoning of given values of imits. [15 pt] 4. 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 and Mare real numbers such that limf(x) = L and limg(x) = M. Let c be a constant. Then, each of the following statements holds: Sum law for limits: lim (f(x) + g(x)) = limf(x) + limg(x)=L+M Difference law for limits: lim (f(x)-g(x)) = limf(x) - limg(x)=L-M Constant multiple law for limits: lim cf(x) = c-limf(x) = cl you - Product law for limits: lim (f(x) g(x)) - limf(x) limg(x)=L-M THE Quotient law for limits: lim : A 100 x(x) Power law for limits lim ((x))" - (lim(x))" =L" for every positive integer n 1-0 Root law for limits: lim √(x) = limf(x) = VL for all L if n is odd and for L 20 if n is even and f(x) > 0. 2f(x)-3g(x) lim x-0 (f(x) + 3)¹/2 Suppose that limf(x) = 1 and lim g(x) = -3. Step lim, foxx) lim2f(x)-3g(x) lim(/(x) + 3)1/² 2limf(x) - 3limg(x) lim(f(x) + 3)¹/2 X40 2limf(x) - 3limg(x) 1/2 lim(f(x) + 3) -31img(x) 2limf(x) - 1/2 (limf(x) + lim3)" 2+9 11 2 (1+3)¹/2 THE = for M0 stitutio Reasoning of given values of imits.

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