[" Q.1(a) For all "x in(0,1)],[" (A) "e^(x)<1+x]

For all x epsilon(0,1)

For all x in (0,1) , then

Let p(x) be a function defined on R such that p'(x) = p' (1 - x) , for all x in [0,1], p(0) = 1 and p (1) = 41. Then int_0^1 p(x) dx equals :

Let p(x) be a function defined on R such that p'(x)=p'(1-x),"for all" x in [0,1],p(0)=1 and p(1)=41."Then" , int_(0)^(1)p(x) dx equals

Let f defined on [0, 1] be twice differentiable such that |f " (x)| <=1 for x in [0,1] ,if f(0)=f(1) then show that |f'(x)|<1 for all x in [0,1] .

Let f defined on [0, 1] be twice differentiable such that |f " (x)| <=1 for x in [0,1] ,if f(0)=f(1) then show that |f'(x)|<1 for all x in [0,1] .

Prove that the function f(x)=x+1/x (x ne 0) is decreasing for all x in (-1, 0) uu (0, 1) .

The set of all possible real values of a such that the inequality (x-(a-1))(x-(a^2-1))<0 holds for all x in (-1,3) is a. (0,1) b. (oo,-1] c. (-oo,-1) d. (1,oo)

The set of all possible real values of a such that the inequality (x-(a-1))(x-(a^(2)-1))<0 holds for all x in(-1,3) is (0,1) b.(oo,-1] c.(-oo,-1) d.(1,oo)

The set of all possible real values of a such that the inequality (x-(a-1))(x-(a^2-1))<0 holds for all x in (-1,3) is (0,1) b. (oo,-1] c. (-oo,-1) d. (1,oo)