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Let f(x)=x^(5)[1/(x^(3))],x!=0 & f(0)=0 ...

Let `f(x)=x^(5)[1/(x^(3))],x!=0` & `f(0)=0` (where [.] represent G.I.F.), Then `lim_(xto0)f(x)`

A

Does not exist

B

1

C

`-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`x-1lt[x]lex`
`1/(eta^(3))-1lt[1/(eta^(3))]le1/(eta^(3))`
`x^(5)(1/(eta^(3))-1)ltx^(5)[1/x^(3)]lex^(2)`
`implieslim_(xto0)x^(5)[1/(x^(3))]=0`
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