Let g(x)= x + 7/x^2 + 5x -14. Determine all values of x at which g is discontinu
ID: 2880197 • Letter: L
Question
Let g(x)= x + 7/x^2 + 5x -14. Determine all values of x at which g is discontinuous, and for each of these values of x, define g in such a manner as to remove the discontinuity, if possible. g(x) is discontinuous at x = (Use a comma to separate answers as needed.) For each discontinuity in the previous step, explain how g can be defined so as to remove the discontinuity. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. g(x) has two discontinuities. The lesser discontinuity cannot be removed. The greater discontinuity can be removed by setting g to be at that value. g(x) has two discontinuities. The lesser discontinuity can be removed by defining g to be at that value. The greater discontinuity cannot be removed. g(x) has two discontinuities and neither can be removed. g(x) has one discontinuity, and it can be removed by defining g to at that value. g(x) has one discontinuity, and it cannot be removed. g(x) has two discontinuities. The lesser discontinuity can be removed by defining g to be at that value. The greater discontinuity can be removed by defining g to be at that value.Explanation / Answer
Rational function is continous for all numbers except where the denominator is zero.
x^2+5x-14=0
(x+7)(x-2)=0
x= -7,2
So, g(x) is discontinous at x = -7,2
=================
lim x--> -7 (x+7)/(x^2+5x-14) =lim x--> -7 (1/(x-2) = -1/9
Option B is correct,
The lesser discontinuity can be removed by defining g to be -1/9 at that value.
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