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Q 1 ) lim x---->∞ (√ x √ x + √x - √ x ) Q 2) lim x---->∞ x 3/2 √ x 3 + 1 - √ x 3 - 1 ans : 1 Q 3) lim x---->∞ 1/ 1-n 4 + 8 / 1-n 4 + ........... + n 3 / 1-n 4 ans: - 1 / 4 ?

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


Q 2) limx---->∞  x3/2 √ x3 + 1   -  √ x3 - 1


ans : 1


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


ans: - 1 / 4


 

Grade:11

2 Answers

Jack sparrow
17 Points
9 years ago

the answer is infinity

Swapnil Saxena
102 Points
9 years ago

Ans 3.

(1+ 8 + 27 + ... + n3)/1-n

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

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