- #1
bundleguide
- 4
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Hi everyone !
I got the weird idea of revisiting my old math books from 20 years ago
and I got stuck on an problem that is probably super easy for most of you.
It's from the chapter where we learn about how to solve limits of the form
[tex]0^0, \infty^0, 1^\infty[/tex]
by transforming an equation like this :
[tex]\lim_{x\rightarrow a} y = f(x)^{g(x)} [/tex]
into this :
[tex]\lim_{x\rightarrow a} \ln y = g(x) \times \ln f(x) [/tex]
etc.
The problem statement, with answer from the book :
[tex]\lim_{x\rightarrow0} \left[(\tan x)/x\right]^{1/x^2} = e^{1/3}[/tex]
The attempt at a solution
It's the last problem of a serie of 50 and I got all the others right !
I really tried by myself, its true !
Anyone can help me on how to find the answer ?
Thanks !
I got the weird idea of revisiting my old math books from 20 years ago
and I got stuck on an problem that is probably super easy for most of you.
It's from the chapter where we learn about how to solve limits of the form
[tex]0^0, \infty^0, 1^\infty[/tex]
by transforming an equation like this :
[tex]\lim_{x\rightarrow a} y = f(x)^{g(x)} [/tex]
into this :
[tex]\lim_{x\rightarrow a} \ln y = g(x) \times \ln f(x) [/tex]
etc.
The problem statement, with answer from the book :
[tex]\lim_{x\rightarrow0} \left[(\tan x)/x\right]^{1/x^2} = e^{1/3}[/tex]
The attempt at a solution
It's the last problem of a serie of 50 and I got all the others right !
I really tried by myself, its true !
Anyone can help me on how to find the answer ?
Thanks !