Expert: Paul Klarreich - 7/10/2007

Question
Hi, Paul.
I´m father the universitary son.
I like help to answer the problem the calculus the mi son
sorry,my english it's no good

The problem is.
Lim
x-> 1   (Sen (pi x))/(x(x+1))

your truly
Mario Monge
Arica-Chile


Answer
Questioner:   Mario Monge
Category:  Calculus
 
Subject:  finding limit
Question:  Hi, Paul.
I´m father the universitary son.
I like help to answer the problem the calculus the mi son
sorry,my english it's no good

The problem is.
Lim
x-> 1   (Sen (pi x))/(x(x+1))

your truly
Mario Monge
Arica-Chile
.......................................
Hola, Mario,

If this is your question:

      sin(pi x)
lim   -----------
x->1    x(x+1)

then it is really not a problem.  The denominator,  x(x+1), does not become zero at the limit, x=1, so this function is CONTINUOUS, and we can just substitute  x = 1:

      sin(pi x)      sin(pi)      0
lim   ----------- =  -------- = ------- = 0
x->1    x(x+1)        1(1+1)       2

I think you may have mistyped something, however.  Check your example again.  Was it:

      sin(pi x)
lim   -----------
x->1    x(x-1)


If it was, then we have more work to do.