Let `g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1))` If `g(x)` is continuous and differentiable for all numbers in its domain then (A) a=b=-4 (B) a=b=4 (C) a=4 and b =-4 (D) a=-4 and b=4

Let f(x)={{:(3x^(2)-4sqrtx+1,"for",xlt1),(ax+b,"for",xge1):} If f(x) is continuous and differentiable for all real values in its domain then

Let f(x)={((x^3+2x^2-x-2)/(x^3-2x^2-x+2), for |x| lt 1),(x^2+ax+b, for |x| ge 1):} be continuous for all x . Now answer the question:The values of a and b are given by (A) a=-8/3,b=-4/3 (B) a=4/3,b=-8/3 (C) a=-4/3,b=-8/3 (D) a=-4/3,b=8/3

Let f(x)={((x^3+2x^2-x-2)/(x^3-2x^2-x+2), for |x| lt 1),(x^2+ax+b, for |x| ge 1):} be continuous for all x . Now answer the question:The values of a and b are given by (A) a=-8/3,b=-4/3 (B) a=4/3,b=-8/3 (C) a=-4/3,b=-8/3 (D) a=-4/3,b=8/3

If lim_(x->oo)((x^2+x+1)/(x+1)-a x-b)=4,t h e n (a) a=1,b=4 (b) a=1,b=-4 (c) a=2,b=-3 (d) a=2,b=3

If lim_(x->oo)((x^2+x+1)/(x+1)-a x-b)=4,t h e n (a) a=1,b=4 (b) a=1,b=-4 (c) a=2,b=-3 (d) a=2,b=3

Let int_o^x(bt cos 4t - a sin 4t)/t^2 dt = (a sin 4x)/x then a and b are given by 1) a=1/4, b = 1 2)a=2,b=2 3) a= -1, b=4 4)a=2,b=4

Let f(x)={(x-4)/(|x-4|)+a ,x 4 Then f(x) is continous at x=4 when a=0,b=0 b. a=1,b=1 c. a=-1,b=1 d. a=-1,b=-1

Let f(x)={(x-4)/(|x-4|)+a ,x 4 Then f(x) is continous at x=4 when a=0,b=0 b. a=1,b=1 c. a=-1,b=1 d. a=-1,b=-1

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 (a) a=10 : b=6 (b) a=4 : b=12 (c) a=12 : b=4 (d) a=6 : b=10

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 (a) a=10 : b=6 (b) a=4 : b=12 (c) a=12 : b=4 (d) a=6 : b=10