" 5.(i) "(x)/(sqrt(a^(2)-x^(2)))

lim_(x rarr1)(sqrt(x^(2)+8)-sqrt(10-x^(2)))/(sqrt(x^(2)+3)-sqrt(5-x^(2)))=

(i) int_0^a sqrtx/(sqrtx+sqrt(a-x)) dx (ii) int_0^5 sqrtx/(sqrtx+sqrt(5-x)) dx (iii) int_0^a (dx)/(x+sqrt(a^2+x^2))

I= int (dx)/( sqrt( 5-x^(2) - 4x) ) .

(i) int (dx)/sqrt(5+4x-x^2) (ii) int (dx)/sqrt(8+3x-x^2)

lim_(x rarr oo)((sqrt(x^(2)+5)-sqrt(x^(2)-3))/(sqrt(x^(2)+3)-sqrt(x^(2)+1)))

Differentiate the following function : (i) (x^(2) - 5x + 6)(x-3) , (ii) (sqrt(x) + 1/(sqrt(x)))^(2) , (iii) (3x^(2) + 2x + 5)/(sqrt(x))

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 .

Evaluate: (i) int(5x+3)sqrt(2x-1)dx (ii) int(x)/(sqrt(x+a)-sqrt(x+b))dx

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

Let I_(n)=int(x^(n))/(sqrt(x^(2)+2x+5))dx then I_(n)=(x^(m-1))/(n)sqrt(x^(2)+2x+5)-lambda I_(n-1)-mu I_(n-2) where lambda,mu and m' are involving n' then