limits

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m,n belongs to I+ then lim xâ†’0 sinXⁿ/(sinX)^m equals to

a. 1 if n<m
b. 0 if n=m
c. n/m
d. 0 if n>m

#Mathematics #Calculus

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Shriya ·2009-06-27 21:58:12

i think it is d
sinxⁿ/(sinx)^m
multiply and divide by xⁿ and x^mwe have
lim _(xâ†’0)x^n-m

case 1
if n<m then limit will be âˆž , ie won't exist
case 2
if n=m then x⁰will be 1 (not zero; as xâ†’0 ,it is not equal to zero)
case 3
if n>m then the limit will be 0

clearly only these cases will exist ,,hence d

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