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

sqrt(5)x^(2)+2x-3sqrt(5)

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))

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

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 .

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

sqrt(3x^(2)-7x-30)-sqrt(2x^(2)-7x-5)=x-5

The value of integral int e^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(5))))dx is equal to e^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(3))))+ce^(x)((1)/(sqrt(1+x^(2)))-(1)/(sqrt((1+x^(2))^(5))))+ce^(x)((1)/(sqrt(1+x^(2)))+(1)/(sqrt((1+x^(2))^(5))))+c none of these