Question
Asked Sep 11, 2019
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Determine the values of x for which f(x) is discontinuous. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x) = 
 
4     if x ≤ 2
16x − 28    if  2 < x < 6
 
x
(x − 18)(x + 3)
  if x ≥ 6

x =

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Expert Answer

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if xs2 4 The given piecewise function is f(x)= {16x-28 if 2x<6 if x6 (x-18)(x+3) Consider the function f(x)=4. The function f(x)=4 is constant function, which is continuous everywhere. That is, the function f(x)=4 is continuous at x <2

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Consider the function f(x)16x-28 if 2<x<6 continuity is is known that, the condition for the It lim f(x) lim f(x)= f(a) x-a Find the left hand side continuity at x 2 lim f(x)lim f(2-h) x-+2 h0 -lim (16(2-h)-28) h0 (16(2-0)-28) - 36-28 =4 Find the right hand side continuity at x 2 lim f(x) lim f(2+h) x-2 = 0 -lim (16(2 h)-28) h0 =(16(2+0)-28) -36-28 -4

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Find the value of the function at x 2 f(2) (16(2)-28) -32-28 - 4 That is, lim f(x)= lim f(x)= f(2) x2 The function is continuous at x 2 Consider the function f(x)x-18)(x+3) if x 26 Find the left hand side continuity at x6 lim f(x)lim f(6-h) h-0 x6 (6-h) i(6-h)-18)((6-h)+3) h-0 1 18

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