diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-7.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-7.tex | 10 |
1 files changed, 10 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-7.tex b/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-7.tex new file mode 100644 index 00000000000..8ee134a9963 --- /dev/null +++ b/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-7.tex @@ -0,0 +1,10 @@ +\documentclass{article} +\begin{document} +\noindent +Applying l'Hopital's rule, one has +\[ \lim_{x\to0}\frac{\ln\sin\pi x}{\ln\sin x} + = \lim_{x\to0}\frac{\pi\frac{\cos\pi x}{\sin\pi x}}{\frac{\cos x}{\sin x}} + = \lim_{x\to0}\frac{\pi\tan x}{\tan\pi x} + = \lim_{x\to0}\frac{\pi/\cos^2 x}{\pi/\cos^2 \pi x} + = \lim_{x\to0}\frac{\cos^2\pi x}{\cos^2 x} = 1 \] +\end{document} |