anonymous
  • anonymous
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. Let f(x) =\frac{2x^2+5 x -7}{x-1} Show that f(x) has a removable discontinuity at x=1 and determine what value for f(1) would make f(x) continuous at x=1. Must define f(1)=
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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. Let f(x) =\frac{2x^2+5 x -7}{x-1} Show that f(x) has a removable discontinuity at x=1 and determine what value for f(1) would make f(x) continuous at x=1. Must define f(1)=
apoorvk
  • apoorvk
first part answer is 2.
apoorvk
  • apoorvk
next part. at x=1, the function should be equal to the functional value at RHL and LHL of 1.

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anonymous
  • anonymous
whats rhl?
anonymous
  • anonymous
|dw:1332638196102:dw|
anonymous
  • anonymous
notice your f can be simplified to look like the line 2x+7 but with the restriction that x is not equal to 1.
apoorvk
  • apoorvk
right hand limit and left hand limit. that is to the right neighbourhood of 1, about (1.00000000.......1). and lhl would be to the left neighbourhood of 1 that is about (0.9999999.....9)
anonymous
  • anonymous
still there?
anonymous
  • anonymous
yep
anonymous
  • anonymous
so what value woulf make f(x) continuous?
anonymous
  • anonymous
stick in x=1 to the simplified expression for f (look in the drawing)
anonymous
  • anonymous
thanks = 9
anonymous
  • anonymous
good

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