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Findthe values of a and bsucht that thefunction fdefined by fx = {{:((x-4)/(|x-4|)+a, if x lt 4),(a+b,if x=4),((x-4)/(|x-4|)+b, if x gt 4):} is a continousfunctionat x = 4 . |
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Answer» At `x = 4, LHL =underset(xrarr4^(-))(lim)(x-4)/(|x-4|)+a` `= underset(hrarr0)(lim)(4-h-4)/(|4-h-4|)+a= underset(hrarr0)(lim)(-h)/(h) +a` `= -1 +a` `RHL = underset(xrarr4^(+))lim(x-4)/(|x-4|)+b` `= underset(hrarr0)(lim)(4+h-4)/(|4+h-4|) +b = underset(hrarr0)(lim)(h)/(h)+b = 1+b` `f(4)=a + b RARR -1+b = a+ b` `rArr -1 +a = a+b` and `1+b= a+ b` `:. b = - 1` and `a =1`. |
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