`f(x)=[(2sin(x-3)/(x-[x]),xgt3),(((a(x^2-7x+12))/(babs(x^2-7x+12))),xlt3),(b,x=3))`
Find the number of ordered pairs (a,b) if f(x) is continuous at x=3

Prove that the function f(x)=x^(2)-7x+3 is continous at x=1,x=2,x=3

If lim_(xto3)(x^(3)+cx^(2)+5x+12)/(x^(2)-7x+12)=l (finite real number), ten

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

f(x)=(2^x+2^(-x)(tanx)sqrt(tan^-1(2x^2-3x+1)))/(7x^2-3x-1)^3 , then find f'(0)

Consider the function. f(x)={((a(7x-12-x^(2)))/(babs(x^(2)-7x+12)),x lt 3),(2^((sin(x-3))/(x-[x])),x gt 3),(b,x=3):} where [x] denotes the greatest integer less than or equal to x .If "S" denotes the set of all ordered pairs (a,b) such that f(x) is continuous at x=3 ,then the number of elements in S is

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is

lim_(x rarr 3) [(2)/(x-3)+(2)/(x^(2)-7x+12)]= ______.

If f(x)={1 , if xlt=3a x+b , if 3