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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. plz help

alok bharti

12 Years agoGrade

1 Answer

Jitender Singh

12 Years ago

Ans:

$f(x) = x^{2}, x = I$

$f(x) = \frac{-k(x^{2}-4)}{2-x}, x \neq I$

$f(x) = -k(x+2), x \neq I$

For function to be continuous

$\lim_{h\rightarrow 0}f(I-h) = I^{2} = \lim_{h\rightarrow 0}f(I+h)$

$\lim_{h\rightarrow 0}-k(2+I-h) = I^{2} = \lim_{h\rightarrow 0}-k(2+I+h)$

$k = \frac{-I^{2}}{I+2}$

I = Integer

Cheers!

Thanks & Regards

Jitender Singh

IIT Delhi

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