IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

deepak2009

_{[x ]}

_{[0 ]} (lnx)/x

spideyunlimited

LIMIT ONLY EXISTS FOR x --> 0⁺

when x tends to 0 from right hand side

lnx = - infinity

and x = very small +ve number nearly 0

so lnx/x = - (very large number tending to infinity) / very small positive number

= - ( very large number still tending to infinity)

= - infinity

deepak2009

how can u use l hospital rule,
it is neither 0/0 form nor inf/inf form
and u have not done diff of denom

iitkgp_bipin

As x tends to zero numerator, lnx tends to -

and denominator, x tends to 0.

So limit is in the form of -

/0 which is not defined.

Hence the limit doesn't exists.

spideyunlimited

but in graphing calculators and softwares this limit is seen on the graph as -infinity ... :S !!!

kishan12

Hey this is not an undetermined form as inf is not cosidered to be undetermined
so answer is straight away inf x (-inf)= -inf

Ans:-inf