" Neglecting "x^(n)" for "n>=2," value of "(1-7x)^((1)/(3))(1+2x)^((3)/(4))" is "

If |x| is so small that x^2 and higher powers of x many be neglected , prove that ((1 + 7x)^(2/3) . (1 - 4x)^(-2))/((4 + 7x)^(1/2)) = 1/2 (1 + 283/24 x)

If |x| is so small that x^2 and higher powers of x many be neglected , prove that ((1 + 7x)^(2/3) . (1 - 4x)^(-2))/((4 + 7x)^(1/2)) = 1/2 (1 + 283/24 x)

If x_(1),x_(2),x_(3),"……" are in A.P., then the value of 1/(x_(1)x_(2))+1/(x_(2)x_(3))+1/(x_(3)x_(4))+"……"1/(x_(n-1)x_(n)) is :

Statement-1: The middle term of (x+(1)/(x))^(2n) can exceed ((2n)^(n))/(n!) for some value of x. Statement-2: The coefficient of x^(n) in the expansion of (1-2x+3x^(2)-4x^(3)+ . . .)^(-n) is (1*3*5 . . .(2n-1))/(n!)*2^(n) . Statement-3: The coefficient of x^(5) in (1+2x+3x^(2)+ . . .)^(-3//2) is 2.1.

Statement-1: The middle term of (x+(1)/(x))^(2n) can exceed ((2n)^(n))/(n!) for some value of x. Statement-2: The coefficient of x^(n) in the expansion of (1-2x+3x^(2)-4x^(3)+ . . .)^(-n) is (1*3*5 . . .(2n-1))/(n!)*2^(n) . Statement-3: The coefficient of x^(5) in (1+2x+3x^(2)+ . . .)^(-3//2) is 2.1.

The value of lim_(x rarr oo)(2x^((1)/(2))+3x^((1)/(3))+4x^((1)/(4))+......+nx^((1)/(n)))/((2x-3)^((1)/(2))+(2x-3)^((1)/(3))+......+(2x-3)^((1)/(n))) is equal to

If the number of solutions of sin^(-1)x+|x|=1cos^(-1)x+|x|=1,tan^(-1)x+|x|=1,cot^(-1)x+|x|=1,sec^(-1)x+|x|=1 and cos ec^(-1)are n_(1),n_(2),n_(3),n_(4),n_(5),n_(6) respectively,then then then then the value of n_(1)+n_(2)+n_(3)+n_(4)+n_(5)+n_(5) is

If x = 1/(2-sqrt3) then find the value of (x^(3) -2x^2 - 7x +4)