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Let f(x)={{:((x^(n)cos((1)/(x)))/(0^(ta...

Let `f(x)={{:((x^(n)cos((1)/(x)))/(0^(tan^(m)x)),,xne0 ),(0,,x=0):}`

A

`nlem`

B

`mltnlem+1`

C

`nlt2m`

D

`nlt2m+1`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xto0)Lim(x^(n)cos((1)/(x)))/(((tanx)/(x))^(m).x^(m))=underset(xto0)Limx^(n-m)cos((1)/(x))`
`:." "n-mgt0` so that f(x) is continuous at x=0
But f(x) is non-derivable at x=0, so
`f'(0)=underset(xto0)Lim(x^(n)cos((1)/(x)))/(((tanx)/(x))^(m).x^(m).x)=underset(xto0)Limx^(n-m-1)cos((1)/(x))`
`n-m-1le0` os that f'(0) does not exist
`n-mle1`
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