`(1/2x^(1/3)+x^(-1/3))^8`

(ii) [(1)/(2)x^(1/3)+x^(-1/5)]^(8)

int_1^8((x^(1/3)-1)(2-x^(2/3)))/x^(1/3)

The co-efficient of x in the expansion of (1-2x^3+3x^5)(1+1/x)^8 is:

If x is so small that x^3 and higher powers of x may be neglected, then ((1+x)^(3/2)-(1+1/(2x))^3)/((1-x)^(1/2)) may be approximated as A. 3x+3/8x^2 B. 1-3/8x^2 C. x/2-3/x^2 D. -3/8x^2

If x is so small that x^3 and higher powers of x may be neglectd, then ((1+x)^(3//2)-(1+1/2x)^3)/((1-x)^(1//2)) may be approximated as a. 3x+3/8x^2 b. 1-3/8x^2 c. x/2-3/xx^2 d. -3/8x^2

Find lim_(x rarr oo) ((1-2x)/(1+8x^3)^(1/3) +2^(-x^7))

Find underset( x rarr oo )("lim") ((1-2x)/((1+ 8x^(3))^(1//3))+2^(-x^(7)))