If x < 4, which of the following statements are true? Justify your answers.:- 2x < 8

If y = x^(x^x) prove that dy/dx = x^(x+x^x) [1/x+(1+logx)logx]

The value of x for which the matrix |(-x,x,2),(2,x,-x),(x,-2,-x)| will be non-singular, are

If f (x) = log x and g (x) = e^X , then (fog) (x) is :

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

Using the properties of determinants, find the value of x, if: {:|(x+2,x+6,x-1),(x+6,x-1,x+2),(x-1,x+2,x+6)|=0

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].

Find the value of x in sqrt(x+2sqrt(x+2sqrt(x+2sqrt(3x))))...=x.

If A = {x: x in Z and x ge 2} , B= {x: x in Z and x le 4} , then A cap B is equal to:

Solve for x: |(x+9,x,x),(x,x+9,x),(x,x,x+9)|=0