HKDSE Mathematics Question Review (Definite Integral)

[dutalatortoise]

Show that, without using L'Hospital's Rule:

[dutalatortoise]

Hint:

You can prove it by Taylor's theorem.

[dutalatortoise]

Solution: Do standard bookworks first.

[dutalatortoise]

Now you should encounter this indeterminate:

Instead of applying L'Hospital's Rule, read the hints again.

[dutalatortoise]

Now by expanding the hints, we shall notice that:

No constant terms for xlnx, i.e. all terms are products of x. Then by putting x=0, we will yield the desired answer:

Q.E.D.

[dutalatortoise]

Postscript: Mathjax is not so intuitive, so I use the below tool to create math pics:

Online LaTeX Equation Editor

[ngfh]

Nice find. Since MathJax is a LaTeX-based renderer, you can actually skip the image-making step. If you copy the raw LaTeX string from that editor and paste it here, MathJax will render it as searchable, scalable text rather than a static image.

[dutalatortoise]

Great to know that.

I wonder when LibreOffice will support LaTeX someday.