(c)[{((-1)/(3))^(2)}^(-2)]^(-1)

lim_(x rarr1)((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/((x+1)^(2))) is equal to 1 (b) ((2)/(3))^((1)/(2))(c)((3)/(2))^((1)/(2))(d)e^((1)/(2))

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n)x^(n) show that, C_(0)-2^(2)*C_(1)+3^(2)*C_(2)-...+(-1)^(n)*(n+1)^(2)*C_(n)=0 (n gt 2)

Let X=[{:(x_(1)),(x_(2)),(x_(3)):}],A=[{:(1,-1,2),(2,0,1),(3,2,1):}] and B=[{:(3),(1),(4):}] .If AX=B, then X is equal to: a) [(1),(2),(3)] b) [(-1),(2),(3)] c) [(-1),(-2),(3)] d) [(-1),(-2),(-3)]

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(2)+C_(4)x^(4)...+C_(n)x^(n),n>=0 prove that C_(0)-2^(2)C_(1)+3^(2)C_(2)+...+(-1)^(n)(n+1)^(2)C_(n)=0

[The value of "int(sqrt(x^(2)+1){log_(e) (x^(2)+1)-2log_(e)x})/(x^(4))dx" is equal to "],[" (a) "(2)/(3)(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))-(2)/(3)}+C],[" (b) "-(1)/(3)(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))-(2)/(3)}+C],[" (c) "(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))+(2)/(3)}+C ]

C_(0)^(2)+1/2C_(1)^(2)+1/3C_(2)^(2)+….+1/(n+1)C_(n)^(2) equals

(2^(2)*c_(0))/(1.2)+(2^(3)*C_(1))/(2.3)+(2^(4)*c_(2))/(3.4)+......+(2^(n+2)*C_(n))/((n+1)(n+2))=

If C_(r) stands for ""^(n)C_(r) , then the sum of the series (2((n)/(2))!((n)/(2))!)/(n!)[C_(0)^(2)-2C_(1)^(2)+3C_(2)^(2)-...+(-1)^(n)(n+1)C_(n)^(2)] , where n is an even positive integers, is: