1) `x-(1)/(2)sqrt(x^(3)+3x^(2)+3x+1)`

If f(x)=cos^(-1)x+cos^(-1){(x)/(2)+(1)/(2)sqrt(3-3x^(2))} then

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

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

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

(d)/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=(1)/(2(1+x)sqrt(x)) (b) (3)/((1+x)sqrt(x))(2)/((1+x)sqrt(x)) (d) (3)/(2(1+x)sqrt(x))

intdx/((1+x)sqrt(3x^2+3x+1))

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

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

Solution of (2+sqrt(3))^(x^(2)-2x+1)+(2-sqrt(3))^(x^(2)-2x-1)=(4)/(2-sqrt(3))are(A)1+-sqrt(3),1(B)1+-sqrt(2),1(C)1+-sqrt(3),2(D)1+-sqrt(2),2