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question on continuity f(x)=x^2, x belongs to set of integers only f(x)=k(x^2-4)/2-x, x does not belong to set of integers. find value of k so that f(x) is continuous.

question on continuity

 

f(x)=x^2, x belongs to set of integers only

 

f(x)=k(x^2-4)/2-x, x does not belong to set of integers.

 

find value of k so that f(x) is continuous.

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,
f(x) = x^{2}, x = I
f(x) = \frac{-k(x^{2}-4)}{2-x}, x \neq I
f(x) = -k(x+2), x \neq I
For function to be continuous
\lim_{h\rightarrow 0}f(I-h) = I^{2} = \lim_{h\rightarrow 0}f(I+h)
\lim_{h\rightarrow 0}-k(2+I-h) = I^{2} = \lim_{h\rightarrow 0}-k(2+I+h)
k = \frac{-I^{2}}{I+2}
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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