Set of all real value of a such that `f(x)=((2a-1)+x^2+2(a+1)x+(2a-1))/(x^2-2x+40)` is always negative is a.`-oo,0` b. `0,oo` c. `-oo,1//2` d. none

The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^2+(a-1)x+2 possesses a negative point of inflection is (-oo,-2)uu(0,oo) (b) {-4/5} (-2,0) (d) empty set

Find the values of a if f(x)=("lim")_(n rarr oo)(a x^(2n)+2)/(x^(2n)+a+1) is continuous at x=1.

The exhaustive set of values of a for which inequation (a -1)x^2- (a+1)x+ a -1>=0 is true AA x >2 (a) (-oo,1) (b)[7/3,oo) (c) [3/7,oo) (d) none of these

The possible values of a such that the equation x^2+2a x+a=sqrt(a^2+x-1/(16))-1/(16),xgeq-a , has two distinct real roots are given by: [0,1] (b) [-oo,0] [0,oo] (d) (3/4,oo)

The value of int_0^oo(x dx)/((1+x)(1+x^2)) is equal to

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cotx/2sin^2x/2 does not possess critical points is (a) (-oo,-4/3) (b) (-oo,-1) (c) [1,oo) (d) (2,oo)

The set of values of a for which a x^2+(a-2)x-2 is negative for exactly two integral x , is a. (0,2) b. [1,2) c. (1,2] d. (0,2]

lim_(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

Let f(x) be differentiable for real x such that f^(prime)(x)>0on(-oo,-4), f^(prime)(x) 0on(6,oo), If g(x)=f(10-2x), then the value of g^(prime)(2) is a. 1 b. 2 c. 0 d. 4