iPad 8:50 PM Previous Answers SCalcET7 2.5047. 36 points My Notes which of the f
ID: 2866151 • Letter: I
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iPad 8:50 PM Previous Answers SCalcET7 2.5047. 36 points My Notes which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for a and is continuous at a. (If an answer does not exist, enter DNE) M-1 a- 1 (a) f(x) O The discontinuity is removable. O The discontinuity is not removable O The discontinuity is removable. O The discontinuity isnot removable sin x (Recall that h(x) means the largest integer that is less than or equal to h(x)) O The discontinuity is removable. The discontinuity is not removable. at a, but it is not a removable discontinuity, there is no function that agrees with f Please try again. If the function To find a continuous function that agrees with a quotient function fand is at a, factorize each part of the quotient function and divide out common factors. Submit Answer Save Progress Practice Another Version View Previous Question Question 9 of 10 View Ned Question Home My Assignments Edension Reques!Explanation / Answer
a)
f(x) = (x^4 - 1) / (x - 1)
f(x) = (x^2 - 1)(x^2 + 1) / (x - 1)
f(x) = (x - 1)(x + 1)(x^2 + 1) / (x -1)
Cancel (x-1)'s :
g(x) = (x + 1)(x^2 + 1) --> This now has no discontinuities
So, since the original discon a = 1 was removed, we choose
"The discontinuity is removable" --> ANSWER
g(x) = (x + 1)(x^2 + 1) ---> ANSWER
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f(x) = (x^3 - x^2 - 72x) / (x - 9)
f(x) = x(x^2 - x - 72) / (x- 9)
f(x) = x(x - 9)(x + 8) / (x - 9)
Cancel the (x-9)'s :
g(x) = x(x + 8)
So, "discon is removable" --> ANSWER
g(x) = x(x + 8) --> ANSWER
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c)
f(x) = [sin(x)]
We know that sin(pi) equals 0
So, for x slightly less than pi --> second quadrant --> So, sine would be +0
For x slightly greater than pi --> third quadrafnt --> So, it would be -0.00001, which would then become -1 because of the Greatest integer function
Therefore, the discontinuity is non-removable ---> ANSWER
g(x) = DNE ---> ANSWER
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