A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or not continuous at x = a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x = a. 5 I if x #0 and x = 2 Let f(x) = 2 if x=0 Show that f(x) has a removable discontinuity at x =0 and determine what value for f(0) would make f(x) continuous at x = 0. Must redefine f(0) = -4x+10 + x(x-2) Hint: Try combining the fractions and simplifying. The discontinuity at x = 2 is actually NOT a removable discontinuity, just in case you were wondering.
A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or not continuous at x = a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x = a. 5 I if x #0 and x = 2 Let f(x) = 2 if x=0 Show that f(x) has a removable discontinuity at x =0 and determine what value for f(0) would make f(x) continuous at x = 0. Must redefine f(0) = -4x+10 + x(x-2) Hint: Try combining the fractions and simplifying. The discontinuity at x = 2 is actually NOT a removable discontinuity, just in case you were wondering.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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Transcribed Image Text:A function f(x) is said to have a removable discontinuity at x = a if:
1. f is either not defined or not continuous at x = a.
2. f(a) could either be defined or redefined so that the new function IS continuous at x = a.
5 -4x+10
+
x(x-2)
I
if x #0 and x # 2
Let f(x) =
if x=0
Show that f(x) has a removable discontinuity at x = 0 and determine what value for f(0) would make
f(x) continuous at x = 0.
Must redefine f(0) =
Hint: Try combining the fractions and simplifying.
The discontinuity at x = 2 is actually NOT a removable discontinuity, just in case you were wondering.
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