The value of `k(k<0)` for which the function `f` defined as `f(x)={((1-cos kx)/(x sin x),x!=0),((1)/(2),x=0):}`
is continuous at `x=0` is :
(A) `+-1`
(B) `-1`
(C) `+-(1)/(2)`
(D) `(1)/(2)`

If f(x)={(ax^2+b ,0lex<1),(4,x=1),(x+3,1ltxge2)) then the value of (a ,b) for which f(x) cannot be continuous at x=1, is (a) (2,2) (b) (3,1) (c) (4,0) (d) (5,2)

let f(x)={(ax+1, if x le 1),(3, if x=1),(bx^2+1,if x > 1)) if f(x) is continuous at x=1 then value of a-b is (A) 0 (B) 1 (C) 2 (D) 4

Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b varies, the range of m(b) is (A) [0,1] (B) (0,1/2] (C) [1/2,1] (D) (0,1]

If f(x)=xsin(1/x) ,\ x!=0 , then the value of the function at x=0 , so that the function is continuous at x=0 , is (a) 0 (b) -1 (c) 1 (d) indeterminate

The value of k which makes f(x)={sinx/x ,x!=0, and k , x = 0 , continuous at x=0 ,is (a) 8 (b) 1 (c) -1 (d) none of these

If the function f(x) defined by f(x)={(log(1+3x)-log(1-2x))/x\ \ \ ,\ \ \ x!=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \k ,\ \ \ \ \ \ \ x=0 is continuous at x=0 , then k= (a) 1 (b) 5 (c) -1 (d) none of these

int_(0)^(1)|2x-1|dx=? (a) 2 (b) (1)/(2) (c) 1 (d) 0

The value of int_0^1lim_(n->oo)sum_(k =0)^n(x^(k+2)2^k)/(k!)dx is: (a) e ^(2) -1 (b) 2 (c) (e ^(2)-1)/(2) (d) (e ^(2) -1)/(4)

The value of x satisfying the equation log_(2)(x^(2)-2x+5)=2 is "(a) 1 (b) 0 (c) -1 (d) 2 "

The value of (lim)_(x->pi//2)(s e c x-t a n x) is a. 1 b . 0 c. 2 d. -1