(1-x^(2))^(12)

If f(x)=int_(1)^(x^(3))(dt)/(1+t^(4)), then f'(x) is equal (6x((1-5x^(2))^(12)))/((1+x^(12))^(12))) (ii) (6x((1+5x^(2))^(12)))/((1+x^(12))^(2))( (iii) -(6x((1-5x^(2))^(12)))/((1+x^(12))^(2)) (iv) none of these

The term without x in the expansion (2x-(1)/(2x^(2)))^(12) is a.495b.-495c.-7920d7920

If x is a cube root of unity other then 1 , then (x+(1)/(x))^(2)+(x^(2)+(1)/(x^(2)))^(2)+.....+(x^(12)+(1)/(x^(12)))^(2)

If x is a cube root of unity other than 1 then (x+(1)/(x))^(2)+[x^(2)+(1)/(x^(2))]^(2)+…+[(x^(12))+(1)/(x^(12))]^(2)=

The series expansion of log[(1 + x)^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]

The series expansion of log_(e) [(1 + x^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]

The term without x in the expansion (2x-1/(2x^2))^(12) is a. 495 b. -495 c. -7920 d. 7920

(x^(2)+(1)/(x))^(12)