Consider the statement : `x (alpha-x) < y (alpha-y)` for all `x,y` with `0 < x < y < 1.` The statements is true

Consider the statement,"If x is an integer and x^2 is even, then x is also even." prove the statement by the contrapositive method.

Consider the statement,"If x is an integer and x^2 is even, then x is also even." Write the converse of the statement.

Consider the statement,"If x is an integer and x^2 is even,then x is also even".(a)Write the converse of this statement.

f (x)= x^(6) -x-1, x in [1,2]. Consider the following statements :

f (x)= x^(6) -x-1, x in [1,2]. Consider the following statements :

Consider the following statements: 1. The function f(x)=|x| is not differentiable at x=1. 2. The function f(x)=e^(x) is not differentiable at x=0. Which of the above statements is/are correct ?

Consider the following statements: I. f(x)=|x-3| is continuous at x=0. II. f(x)=|x-3| is differentiable at x=0. Which of the statements given above is/ are corrent?

Consider the following statements 1 f(x)=In x is an increasing funciton on (0,oo) 2 f(x) =e^(x)-x(In x) is an increasing function on (1,oo) Which of the above statement is / are correct ?

Consider the following statements: I. The function f(x)=|x| is not differentiable at x = 1 II. The function f(x)=e^(x) is differentiable at x = 0 Which of the above statements is/are correct?

Consider the function: f(x)={{:((alphacosx)/(pi-2x),"if "xne(pi)/(2)),(3,"if "x=(pi)/(2)):} Which is continuous at x=(pi)/(2) , where alpha is a constant. What is the value of alpha ?