`f(x)={a-bx if x<1,8 if x=1, b-2ax if x>1`, `lim_(x->1^-) f(x)=f(1),lim_(x->1^+) f(x)=f(1)` find `a=`

If f(x)=xtan^(-1)x , then lim_(xto1)(f(x)-f(1))/(x-1)=

if f(x)={-1,AA x 2} then (i)f(x)=1, (ii) lim_(x rarr-1^(+))f(x)=1 (ii) lim_(x rarr2^(+))f(x)=-1(iv)lim_(x rarr2^(-))f(x)=0

The function f(x) =p [x+1] +q [x-1] where [x] is the greatest integer function, and lim _(xto1+) f(x) =lim _(x to 1-) f(x)= f(1) when-

Suppose f(x)={(a+bx, x 1):} and if lim_(xto1) f(x)=f(1), what are the values of a and b?

Suppose f(x)={(a+bx, x 1):} and if lim_(xto1) f(x)=f(1) , what are the values of a and b?

If the function f(x) satisfies (lim)_(x->1)(f(x)-2)/(x^2-1)=pi, evaluate (lim)_(x->1)f(x)

Statement - 1: The function f(x) = {x}, where {.} denotes the fractional part function is discontinuous a x = 1 Statement -2: lim_(x->1^+) f(x)!= lim_(x->1^+) f(x)

Suppose f(x)={:{(a+bx,x lt 1) ,(4,x=1), (b-ax,x gt 1):} and if lim_(x to 1) f(x)=f(1). What are possible values of a and b?

lim_(xto1)f(x) if f(x)={(2x-1, xle1), (2x+1, xgt):}

If f(x)={(a+bx,x 1):} and lim_(xrarr1)f(x)=f(1) , then find the value of a and b.