If `f(x)={[(1-sin^2x)/(3cos^2x),xltpi/(2)],[a,x=pi/2],[(b(1-sinx))/((pi-2x)^2),x gtpi/2]}` then f(x) is continuous at `x=pi/2`,if
(a)`a=1/3,b=2` (b) `a=1/3,=8/3` (c)`a=2/3,b=8/3` (d) none of these

If f(x)={(((1-sin^(3)x))/(3cos^(2)x)",",x lt (pi)/(2)),(a",",x=(pi)/(2)),((b(1-sinx))/((pi-2x)^(2))",",x gt (pi)/(2)):} is continuous at x=(pi)/(2) , then the value of ((b)/(a))^(5//3) is

Let f(x)={(1-sin^3x)/(3cos^2x) if x pi/2 find a and b. .

If f(x)=(1-sinx)/((pi-2x)^2) ,when x!=pi/2 and f(pi/2)=lambda, the f(x) will be continuous function at x=pi/2 ,where lambda=? (a) 1/8 (b) 1/4 (c) 1/2 (d) none of these

If f(x)=f(x)={(sin(a+1)x+sinx)/(x), ,x<0,c \ at x=0, (sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,f(x) is continuous at x=0,t h e n (a). a=-3/2,b=0,c=1/2 (b) a=-3/2,b=1,c=-1/2 (c) a=-3/2,b in R-[0],c=1/2 (d) none of these

Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2dot Then, f(x) has a minimum at x= (a+b+c)/3 (b) 1/2 (c) 1/8 (d) none of these

f(x)={{:(((3)/(2))^((cot 3x)/(cot 2x)), 0 le xlt (pi)/(2)),(b+3, x =(pi)/(2)),( (1+|cotx|)^((a tan x|)/b), (pi)/(2) lt xlt pi):} is continuous at x= pi/2 , then

If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x >pi/2 , then which of the following holds? (a) f is continuous at x=pi//2 (b) f has an irremovable discontinuity at x=pi//2 (c) f has a removable discontinuity at x=pi//2 (d)None of these

Let f(x)={1/(|x|)for|x|geq1a x^2+bfor|x|<1iff(x) is continuous and differentiable at any point, then a=1/2,b=-3/2 (b) a=-1/2,b=3/2 a=1, b=-1 (d) none of these

Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2 . Then, f(x) has a minimum at x= (a+b+c)/3 (b) 3sqrt(a b c) (c) 3/(1/a+1/b+1/c) (d) none of these

If sin^(-1)x-cos^(-1)x=pi/6 , then x= (a) 1/2 (b) (sqrt(3))/2 (c) -1/2 (d) none of these