Posted by **MS** on Wednesday, March 12, 2014 at 6:13am.

Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc.

1. Int. of (xlogx)dx from 0 to 1. Indefinite Int. comes to [x^2/2*logx-x^2/4].

Applying limits, Def. Int. =(1/2log1-1/4) – [lim as x->0 of(x^2/2*logx-0)] = -1/4, which is the required answer, if I take limit of (x^2/2*logx)=0 as x->0 ……(A).

2. Int. of (x^2*e^-x)dx from 0 to infinity. Indefinite Int. comes to [e^-x(-x^2-2x-2)].

Applying limits, Def. Int.= lim as x->infinity, of [(-x^2-2x-2)/ e^x] – [lim as x->0 of [ (-x^2-2x-2) /e^x *] = 2, which is the required answer, if I take limit of [1/e^x(-x^2-2x-2]=0 as x->infinity ……(B).

Is it possible to deduce these limits without L’Hopital’s Rule, Squeeze Theorem etc. ?

## Answer This Question

## Related Questions

- Calculus - Following 2 questions are from a book at a point where L’Hopital’s ...
- calculus, limits, l'hopital - Using l'hopital's rule, find the limit as x ...
- calculus, limits, l'hopital - Using l'hopital's rule, find the limit as x ...
- limit calc question - 2 questions!!! 1. Limit X approaching A (X^1/3-a^1/3)/ x-a...
- Calclulus - L'Hopital's Rule - Evaluate the limit as x -> Infinity [5x-sqrt(...
- Calculus - I am trying to solve the following L'hopital's limits question below...
- calculus - Suppose that f(x) is bounded: that is, there exists a constant M ...
- calculus - It is known that x 2 + 4x ≤ f(x) ≤ -x 2 -4x the interval...
- calculus - This is a question related to L'hopital's rule. lim x -> -infinity...
- Calculus - This is a question related to L'hopital's rule. lim x -> -infinity...

More Related Questions