Question

lim x to 1 of (sin (x*pi))/(x-1)

Answer 1

Ahhhh without the use of L'opithals rule!!

Answer 2

Have to ask the smart people.

Answer 3

make the substitution
\(u=x-1\)
the limits change
as \(x\to1\), \(x-1\to0\implies u\to0\)

Answer 4

then it becomes a standard limit!

Answer 5

It will become lim u to 0 of sen((u+1)pi)/u right?

Answer 6

yes. but then you can expand that
\[\sin(u+1)\pi=\sin(u\pi+\pi)=-\sin(u\pi)\]

Answer 7

I'm really sorry. After that u'll get - sin(u*pi)/u then what? :(

Answer 8

that is a standard form remember?

Answer 9

Lim u to 0 of sin u/ u is 1 but in here we have pi multipling inside the factor not outside (sin (u*pi) not pi*sin(u) )right?

Answer 10

exactly.. so, multiply and divide by "pi"
this will create a "pi*x" at the denominator

Answer 11

Omg, now i see it. Sorry man thx a lot!!!

Answer 12

no problemo.