Question

Find limit
lim x-> 1[(1/x-1)-(1/lnx)]

Answer 1

Not sure if this is correct, but as x approaches one from the left I'm assuming, your first term becomes 1 divided by a tiny negative number that decreases. It would be safe to say then that your first term become negative infinity as x approaches 1. Same goes with your second term as x approaches 1, natural log becomes very tiny. Thus 1 divided by a positive tiny number goes to positive infinity. Your left with (-infinity - infinity) which is just [-infinity] as x approaches one, but never becomes one.