If `f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0` and `f(0)=1` is continuous at `x=0` then the value of `m+n` is a. 2 b. 3 c. -3 d. 7

If f(x)=(acos x-cos b x)/(x^2),x!=0a n df(0)=4 is continous at x=0, then the ordered pair (a ,b) is (+-1,3) b. (1,+-3) c. (-1,-3) d. (-1,3)

If f(x)={(sin(2x^2)/a+cos((3x)/b))^a b//x^2,x!=0e^3, x=0 is continuous at x=0AAb in R then minimum value of a is -1//8 b. -1//4 c. -1//2 d. 0

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these

Let : f(x)={(sina x^2)/(x^2),x!=0 3/4+1/(4a),x=0 for what values of a is f(x) continuous at x=0?

If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0) , and f(0) = 0, then the value of f(1) is

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a) -1 (b). 1 ( c.) 0 (d). 2

If the function f: Rsetminus {0}vec given by f(x)=1/x-2/(e^(2x)-1) is continuous at x=0, then find the value of f(0)

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

If x satisfies x^(2)-2x cos theta +1=0 , then the value of x^(n)+((1)/(x^n)) is