(xv)2x^(2)-(5)/(6)x+(1)/(12)

(x+1)/(2)+(x-1)/(3)=(5)/(12)(x-2)

Show that the sum of the coefficients of x^(-6) and x^(-1) in (5x^(2)-(7)/(x^(3)))^(12) is positive.

If (1+x-2x^(2))^(6) = 1 + a_(1)x+a_(2)x^(2) + "……" + a_(12)x^(12) , then find the value of a_(2) + a_(4) +a_(6)+ "……" + a_(12) .

5(4x+5)=5(x+2(1)/(2))-(1)/(2)(7x+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 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)-...]