1-(9)x^(3)-x^(2)-(2+sqrt(2))x+sqrt(2)

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

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

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

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

The value of lim_(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))" is "

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

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))