Find the relation between a and b if `lim_(x to 3) f(x)` exists where `f(x) ={ {:( ax+b , "if " x gt 3),(3ax - 4b +1 , "if " x lt 3):}`

Find the relation between a and b if lim_(xto3)f(x) exists where f(x)={{:(ax+1," if "xle3),(bx+3," if "xgt3):}

Find the relationship between a and b so that the function f defined by f(x)={{:(ax+1-2," if "x le 3),(bx+3," if "x gt 3):} is continuous at x=3.

verify the existence of lim_(x to 1) f (x) , where f(x) ={{:((|x-1|)/(x-1) , "for" x ne 1),(0 , ", for " x=1):}

Verify the existence of lim_(x to 3) f(x) , where f(x)={:{(|x-3|/(x-3),for , xne 3),(0, for ,x =3):}

Verify the existence of lim_ (x to 1)f(x) , where f(x)={{:((|x-1|)/(x-1),"for" x ≠ 1),(0,"for" x=1):}

Find lim_(x rarr 3)f(x),where f(x)=[|x-3|]/[x-3] ,xne3 .

Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x