1.

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

Answer»

`nlem`
`mltnlem+1`
`nlt2m`
`nlt2m+1`

Solution :`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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