英文問題 to sth

Question 1:

To can be a preposition or it can be part of a to-infinitive.

Your comments are invaluable to improving our programs.

In the above sentence, “to” serves as a preposition.

Format:
invaluable + to (preposition) + noun/noun phrase

Your advice has been invaluable to all the students.
“all the students” is a noun phrase.

After the preposition “to”, we can put a gerund clause instead of a noun phrase.
An authoritative grasp of English is invaluable to obtaining many jobs.

Question 2:

字典註明某D字後面要+(to sth), 呢個sth可以係gerund

I'm looking forward to seeing you. (seeing is a gerund)
I object to paying that much for milk. (paying is a gerund)
She is used to working late at night. (working is a gerund)

Be careful.
She used to work late at night. (to work ~ to-infinitive)

Comment:
你要分得出 to 什麼時候做 preposition, 什麼時候做 to-infinitive. 英語文法書籍說 to 後面可以 replace with a noun/noun phrase, to 便是preposition.
如果是這麼簡單, 三言兩語解答了.你匿名, space 所限,有機會,再討論

It will be invaluable to have a "preview" before final submission.
~ from “British Medical Journal”

Your comments are invaluable to improving our programs.= 您的意見，以改善我們的計劃是非常寶貴的。