Homework Sourseevaluate and show all the steps of lim when x goes to 1 from
evaluate and show all the steps of
lim when x goes to 1 from rigth 0 of (x^2)ln x
lim when x goes to 1 from rigth 0 of (x^2)ln x
Solution
L = lim ( x ? 0+ ) x.( ln x )² = lim ( x ? 0+ ) [ ( ln x )² / ( 1/x ) ].......Indet. Form : 8/8 ......................................… Diff...top and bottom separately w.r.t. x, by L\' Hopital\'s Rule, L = lim ( x ? 0+ ) [ 2* ln x* ( 1/ x ) / ( - 1/ x² ) ] ...= lim ( x ? 0+ ) ( - 2* x* ln x ) ...= lim -2* ( ln x ) / ( 1 / x ) .........again indet. form : 8/8 ...= lim -2* ( 1/x ) / (- 1/x² ) ..........again using L\' Hopital ...= lim ( 2x ) ...= 0. .......................Ans.
