" If (i) "x^(x)

If (logx)/(y-z) = (logy)/(z-x) = (logz)/(x-y) , then prove that (i) x^(x) . y^(y) . z^(z) = 1 .

Differentiate the following functions with respect to x : (i) (x^x)^x

Solve for x(i)|x^(3)-1|>=1-x

Find the value of x if i) |[x^(2)-x+1,x+1],[x+1,x+1]|=0

Find the value of (i)x^(3)-x^(2)+x+46, if x=2+3i.

Find the derivative of the following function with respect to 'X' (i) x^(4) (ii) x^(-3) (iii) 3x^(2)

Convert the following points from polar coordinates to the corresponding Cartesian coordinates. (i) ( i i ) (iii)(( i v ) (v)2, (vi)pi/( v i i )3( v i i i ) (ix) (x))( x i ) (xii) (ii) ( x i i i ) (xiv)(( x v ) (xvi)0, (xvii)pi/( x v i i i )2( x i x ) (xx) (xxi))( x x i i ) (xxiii) (iii) ( x x i v ) (xxv)(( x x v i ) (xxvii)-sqrt(( x x v i i i )2( x x i x ))( x x x ) , (xxxi)pi/( x x x i i )4( x x x i i i ) (xxxiv) (xxxv))( x x x v i ) (xxxvii)

Differentiate the following functions with respect to x:( i (x^(x))(x^(x))^(x)

Consider the identity function I_(N):N to N defined as I _(N) (x)=x AA x in N. Show that although I _(N) is onto but I _(N) + I _(N) : N to N defined as (I _(N) + I _(N)) (x) = I _(N) (x) + I _(N) (x) = x +x = 2x is not onto.