9*(4x+2)sqrt(x^(2)+x+1)

Lt_(x to oo) (sqrt(3+9x^(2))+sqrt(4x^(2)-1))/(sqrt(1+16x^(2))-sqrt(9x^(2)+2))=

underset(x to oo)lim (sqrt(1+9x^(2))+sqrt(x^(2)-1))/(sqrt(1+9x^(2))-sqrt(x^(2)-1))=

int(x^(4)-1)/(x^(2)sqrt(x^(2)+x^(2)+1))dx=sqrt(x^(2)+(1)/(x^(2))+1)+C(sqrt(x^(2)+x^(2)+1))/(x^(2))+C(sqrt(x^(4)+x^(2)+1))/(x)+C(d) none of these

The Range of sqrt(-x^(2))+sqrt(x^(2)-4x+9) is

lim_(x rarr2)((sqrt(x^(2)-4x+5)-1)((x+2)^(9/2)-512))/((x-2)(sqrt(x^(2)-4x+20)-4))

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 .

Choose the correct answer int sqrt(x^(2)-8x+7)dx(A)(1)/(2)(x-4)sqrt(x^(2)-8x+7)+9log|x-4+sqrt(x^(2)-8x+7)|+C(1)/(2)(x+4)sqrt(x^(2)-8x+7)+9log|x+4+sqrt(x^(2)-8x+7)|+C(C)(1)/(2)(x-4)sqrt(x^(2)-8x+7)-3sqrt(2)log|x-4+sqrt(x^(2)-8x+7)|+(1)/(2)(x-4)sqrt(x^(2)-8x+7)-((9)/(2))log|x-4+sqrt(x^(2)-8x+7)|

lim_(x rarr oo)((sqrt(1+25x^(2))+sqrt(9x^(2)-1))/(sqrt(1+25x^(2))-sqrt(9x^(2)-1)))=

underset(x to oo)lim (sqrt(1+25x^(2))+sqrt(9x^(2)-1))/(sqrt(1+25x^(2))-sqrt(9x^(2)-1))