(a) Determine whether each of the following functions is continuous at 2.Name any results or rules that you use. You may use the basiccontinuous functions listed in Theorem D51 from Unit D4.(i) f(x) =(ii) f(x) =(iii) f(x) =2-3x+x²,x² - 3,.2x≤ 2,x > 2.[(x - 2)² sin (2)10,sin(x), x≤ 2,x² - 4,x > 2.x = 2,p is given by23x²-3x+1.x = 2.(b) The polynomialp(x) = 3x³(i) Determine a real number M such that p has no zeros outside theinterval (-M, M), and exactly three zeros in (-M, M).(ii)Determine an open interval of length in R that contains exactlyone zero of p. Theorem D51 Basic continuous functionsThe 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.

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(a) 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. (i) f(x)= (ii) f(x)= (iii) f(x) = 2-3x+x², | x² – 3, x≤ 2, x > 2. (x - 2)² sin (x-2), 10. (sin(TI), T≤2, ²-4, x > 2. x 2, x = 2.

(a) 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. (i) f(x)= (ii) f(x)= (iii) f(x) = 2-3x+x², | x² – 3, x≤ 2, x > 2. (x - 2)² sin (x-2), 10. (sin(TI), T≤2, ²-4, x > 2. x 2, x = 2.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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