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 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) = (2x + 3 sin x)/( 3x + 2 sin x), x ne 0 is continuous at x = 0 , then find f(0)

Let f(x)={(1+3x)^(1/x), x != 0e^3,x=0 Discuss the continuity of f(x) at (a) x=0, (b) x=1

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?

The minimum value of e^(2x^2-2x+1)sin^2x is e (b) 1/e (c) 1 (d) 0

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 x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+c

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

The function f(x)=sin^(-1)(cosx) is (a) discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these

"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).