" 5."(2x+5)/(sqrt(x^(2)+3x+1))

int(2x+5)/(sqrt(x^(2)+3x+1))

Find the first 5 terms,in ascending powers of x, in the expansion of (2+3x)/(sqrt(1-5x^(2)))

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 .

" 5."int ((2x+1)/sqrt(3x+2))dx

lim_ (x rarr oo) (sqrt (3x ^ (2) +1) -sqrt (2x ^ (2) -3x + 5)) / (7x + 2) =

THe value of x which satisfy the equation (sqrt(5x^(2)-8x+3))-sqrt((5x^(2)-9x+4))=sqrt((2x^(2)-2x))-sqrt((2x^(2)-3x+1))

(3x+sqrt(9x^(2)-5))/(3x-sqrt(9x^(2)-5))=5

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

((sqrt(x))^((3)/(5))times(sqrt(x))^((2)/(5))+2sqrt(x))/(2(sqrt(x))^((2)/(3))times(sqrt(x))^((1)/(3))+sqrt(x))=

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)