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Example of Mathematics Assignment Help , Mathematics Homework Help
Finding the Limit of expression given by (1+n)3-1)/n when nà 0
Method –I to find the limit of function
(1+n)3-1)/n when n-> 0
Solution:
Since Num/ Den = 0/0 if we put n = 0
Thus we can apply L' Hospital's Rule
to find the Limit of expression
( 1 + n )³ - 1
=> Lt n₋₀ ____________
n
N' = 3 ( 1 + n ) 2 - 0 = 3 ( 1 + n )2
N' Lt n₋₀ = 3
Denominator (D ') = dn/dn = 1
So According to L'Hospital Rule
( 1 + n )³ - 1
=> Lt n->0 _________________
n
Lt n->0 N'/D' = 3/1
= 3 Answer
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Method –II to find the limit of function
(1+n)3-1)/n when n-> 0
Solution:
Since ( 1 + n )³ - 1
___________.
= [( n³ + 1 + 3 n² + 3 n ) – 1]/n
= ( n³ + 3 n² + 3 n )
= ______________
n
Hence Limit of the function is given by
( n³ + 3 n² + 3 n )
= Lt n₋₀ ___________________
n
=> Lt n₋₀ (n2 + 3 n + 3)
=> ( 0 ) 2 + 3 ( 0 ) + 3 = 3
Answer
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