" 3.(i) "x sqrt(x^(2)-1)

The domain and range of real function f if (i) f(x)=sqrt(1-x^(2))(ii)sqrt((x-1)(x-3))(iii)sqrt(4x-x^(2)-3)

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

Differentiate each of the following functions with respect to x:( i) sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))

Evaluate: ( i )(x+1)/(sqrt(2x+3))dx (ii) int x sqrt(x+2)dx

" 2.(i) sqrt(3x+1)-sqrt(x-1)=2

The value of the integral I=int_(1)^(oo) (x^(2)-2)/(x^(3)sqrt(x^(2)-1))dx , is

The value of the integral I=int_(1)^(oo) (x^(2)-2)/(x^(3)sqrt(x^(2)-1))dx , is

Evaluate: (i) int(4x+2)sqrt(x^(2)+x+1)dx (ii) int(4x+3)/(sqrt(2x^(2)+3x+1))dx