Q 1 ) lim_x---->∞ (√ x √ x + √x - √ x )

Q 2) lim_x---->∞ x^3/2 √ x³ + 1 - √ x³ - 1

ans : 1

Q 3) lim_x---->∞ 1/ 1-n⁴ + 8 / 1-n⁴ + ........... + n³ / 1-n⁴

ans: - 1 / 4

?

the answer is infinity

Ans 3.

(1+ 8 + 27 + ... + n³)/1-n⁴ 

Since 1³+2³+3³+...+n³ = (n(n+1))²/4   then

the expression becomes  (n(n+1))²/4(1-n⁴)

= ((n)²(n+1)²⁾/4(1-n⁴)

dividing the whole expression ny n⁴ . Now the expression is 

=(1)(1+1/n²))/4(1/n⁴-1)

= No since n->infinity 1/n tends to 0 thus byu using direct substitutions 

= 1/-4 =-1/4