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If m,n inN,lim(xto0) (sinx^(n))/((sinx)^...

If `m,n inN,lim_(xto0) (sinx^(n))/((sinx)^(m))` is

A

`1 if n>m`

B

`0 if n=m`

C

`0 if n>m`

D

`n/m`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`L=underset(xto0)lim(sinx^(n))/((sinx)^(m))=underset(xto0)lim((sinx^(n))/(x^(n))x^(n))/(((sinx)^(m))/(x^(m))x^(m))=underset(xto0)limx^(n-m)`
If `n=m`, then
`L=("a very small value near to zero")^("exactly zero")=1`
If `ngtm`, then
`L=("a very small value near to zero")^("Positive integer")=0`
If `nltm`, then
`L=("a very small value near to zero")^("negative integer")=oo`
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