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Let lim(x to 0) f(x) be a finite number...

Let `lim_(x to 0) ` f(x) be a finite number, where
`f(x) = ("sin" x + ae^(x) + be^(-x) + cln (1 + x))/(x^(3))` a,b,e in R`

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{:("Column-I","Column-II"),(A.f(x) = (1)/(sqrt(x -2)),p.lim_(x to 0)f(x) =1),(B. f(x) = (3x - "sin"x)/(x + "sin" x), q. lim_(x to 0)f(x) = 0),(C.f(x) = x "sin"(pi)/(x) f(0)=0,r.lim_(x to oo) f(x) = 0),(f(x) = tan^(-1) (1)/(x),s.lim_(x to 0) "does not exist"):}