" 1."(3x^(2)-4x+5)/(sqrt(x))

int_(0)^(1)((3x^(2))/(sqrt(1-x^(6)))+(4x^(3))/(sqrt(1-x^(8)))+(5x^(4))/(sqrt(1-x^(10)))+...." to "n" terms ")dx=

Which of the following expressions are polynomials ? In case of a polynomial , write its degree. (i) x^(5)-2x^(3)+x+sqrt(3) (ii) y^(3)+sqrt(3)y (iii) t^(2)-(2)/(5)t+sqrt(5) (iv) x^(100)-1 (v) (1)/(sqrt(2))x^(2)-sqrt(2)x+2 (vi) x^(-2)+2x^(-1)+3 (vii) 1 (viii) (-3)/(5) (ix) (x^(2))/(2)-(2)/(x^(2)) (x) root(3)(2)x^(2)-8 (xi) (1)/(2x^(2)) (xii) (1)/(sqrt(5))x^(1//2)+1 (xiii) (3)/(5)x^(2)-(7)/(3)x+9 (xiv) x^(4)-x^(3//2)+x-3 (xv) 2x^(3)+3x^(2)+sqrt(x)-1

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 .

Which of the following expressions are polynomials ? In case of a polynomial write its degree. (i) x^(3)-5x+2 (ii) y^(2)+sqrt(2)y-sqrt(5) (iii) 2sqrt(x)+7 (iv) -6 (v) 4t^(2)+(1)/(6)t+2sqrt(3) (vi) z^(2)+(5)/(z^(2))+1 (vii) (1)/(3x) (viii) 1-sqrt(5x) (ix) (1)/(4x^(-2))+3x+5 (x) (6sqrt(x)+x^(3//2))/(sqrt(x))

Differentiate sqrt((x-3) (x^(2) + 4))/sqrt((3x^(2) + 4x + 5)) w.r.t x.

lim_(x=oo)(sqrt(x^(2)+1)-3sqrt(x^(2)+1))/(4sqrt(x^(4)+1)-5sqrt(x^(4)-1)) is equal to

If x+(1)/(x)=(sqrt(2))/(3+sqrt(5)) then, x^(4)+(1)/(x^(4))