- #1
Jarfi
- 384
- 12
Struggling with this limit value
Calculate lim((e^x-1)/x)^(1/sin(x)) where x[itex]\rightarrow0[/itex]
Maclaurin series.
sin(x)/x -----> 1 when x->0 (possibly)
(e^x-1)/x)^(1/sin(x) = ((x+x^2/2+x^3H(x))/x)^(1/sin(x)) =((1+x/2+x^2H(x))/x)^(1/sin(x))
Then getting something like:
1+(1/sinx)C(1)*(1+x/2+x^2H(x))/x) + (1+x/2+x^2H(x))/x)^2*(1/sinx)C(2)
which results in total chaos.
Anybody have a SIMPLE solution?
p.s sorry for the lack of readability, writing math in Physicsforums is a F-ing pain. I mean what the H is [it0ex]\rightharp0oonup[/it0ex] and [itex0]\frac{}{0}[/itex0] telling me.
Homework Statement
Calculate lim((e^x-1)/x)^(1/sin(x)) where x[itex]\rightarrow0[/itex]
Homework Equations
Maclaurin series.
sin(x)/x -----> 1 when x->0 (possibly)
The Attempt at a Solution
(e^x-1)/x)^(1/sin(x) = ((x+x^2/2+x^3H(x))/x)^(1/sin(x)) =((1+x/2+x^2H(x))/x)^(1/sin(x))
Then getting something like:
1+(1/sinx)C(1)*(1+x/2+x^2H(x))/x) + (1+x/2+x^2H(x))/x)^2*(1/sinx)C(2)
which results in total chaos.
Anybody have a SIMPLE solution?
p.s sorry for the lack of readability, writing math in Physicsforums is a F-ing pain. I mean what the H is [it0ex]\rightharp0oonup[/it0ex] and [itex0]\frac{}{0}[/itex0] telling me.
Last edited:
