12 4 - x2 x2 + 6x + 8 Consider the rational function R(x) { R(x)...

 

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12 4 - x2 x2 + 6x + 8 Consider the rational function R(x) { R(x) = [ (4 - x^2) / (x^2 + 6x + 8) ] } a) Limit Definition of Continuity Apply the Limit Definition of Continuity to verify R(x) is continuous at each of the following points: x = 0, x = -1, x= 3 b) Why continuous on domain Extend to general x-a to explain why continuous on the domain. QUESTION 13 discontinuities: identify and classify Consider the rational function R(x) given below { R(x) = [ (2x^2 + 3x + 1)/ (x^2 + x-2)] } a) Evaluate the one sided limits { lim_{x -> -2^-} R(x) lim_{x -> -2^+} R(x) b) Use these to determine the type of discontinuity at x= - 2. c) Evaluate the one sided limits { lim_{x -> 1^-} R(x) lim_{x -> 1^+} R(x) d) Use these to determine the type of discontinuity at x= 1. 12 4 - x2 x2 + 6x + 8 Consider the rational function R(x) { R(x) = [ (4 - x^2) / (x^2 + 6x + 8) ] } a) Limit Definition of Continuity Apply the Limit Definition of Continuity to verify R(x) is continuous at each of the following points: x = 0, x = -1, x= 3 b) Why continuous on domain Extend to general x-a to explain why continuous on the domain. QUESTION 13 discontinuities: identify and classify Consider the rational function R(x) given below { R(x) = [ (2x^2 + 3x + 1)/ (x^2 + x-2)] } a) Evaluate the one sided limits { lim_{x -> -2^-} R(x) lim_{x -> -2^+} R(x) b) Use these to determine the type of discontinuity at x= - 2. c) Evaluate the one sided limits { lim_{x -> 1^-} R(x) lim_{x -> 1^+} R(x) d) Use these to determine the type of discontinuity at x= 1.