" (1v) "x^(6)+x^(4)+x^(2)+1," when "x=(1+i)/(sqrt(2))" ."

Evaluate the following: x^(6)+x^(4)+x62=1, when x=(1+i)/(sqrt(2))

Evaluate the following: x^6+x^4+x^2+1,\ w h e n\ x=(1+i)/(sqrt(2))

Evaluate the following: x^(4)=4x^(3)+6x^(2)+4x+9, when x=-1+i sqrt(2)

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

If f(x)= {(x^2,"when" ,xlt0),( x ," when", 0lexlt1),( 1/x ," when", x gt1):} F i n d : (i) . f(1//2) (ii) . f(-2) (iii) . f(1) (iv) . f(sqrt(3)) (v) . f(-sqrt(3))

Expand using binomial theorem: (i) (1-2x)^(4) " " (ii) (x+2y)^(5) (iii) (x-(1)/(x))^(6) " "(iv) ((2x)/(3)=(3)/(2x))^(5) (v) (x^(2) +(2)/(x))^(6)" "(vi) (1+(1)/(x^(2)))^(4)

Differentiate each of the following functions with respect to x:( i) sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))

int (1+x^(2))/(1-x^(2)).(dx)/(sqrt(1+x^(4)))=(1)/(sqrt(2))log|(sqrt(1+x^(4))+xsqrt(2))/(1-x^(2))|+c