CSIR NET MATHEMATICS | Real Analysis | Simplest Example L’Hospital Rule DEC 2011

Welcome friends, in this video we are going to discuss the problem of linear algebra from CSI and NAIT December 2011. Example, which of the following statement is true? First option, limit x tends to infinity log x divided by x power 1 by 2 equal to 0 and limit x tends to infinity log x divided by x is equal to infinity. In the second option, first limit has value infinity and the second limit has value 0. In the third option both the limit has value 0 and in the fourth option first limit has value 0 but second limit does not exist. First it is a problem of indeterminate form. Identify indeterminate form of first limit which is log x divided by x power 1 by 2. If you put x is equal to infinity then log x approach to infinity and x power 1 by 2 approach to infinity. So it is infinity by infinity. By L'Hospital rule limit x tends to infinity f x divided by f x infinity by infinity form then the result is limit x tends to infinity f dash x divided by g dash x that means derivative of numerator divided by derivative denominator so derivative numerator log x is 1 upon x and derivative denominator x power 1 by 2 is 1 upon 2 into x power 1 by 2 if we simplify then we have 2 divided by x power 1 by 2 as x approach to infinity 1 upon x power 1 by 2 approach to 0 therefore limit as value 0 now for the second limit x tends to infinity log x divided by x so it is also in the form of infinity by infinity and we apply the L'Hospital rule so it is 1 upon x divided by 1 as limit x tends to infinity 1 upon x approach to 0 so its value is 0 option number 3 which says that both the limit as value 0 is correct thanks for watching for more videos like share subscribe please the bell icon of next gen