Question: So, a teacher explained to me that 究竟 is a more formal way of saying 到底. However, I'm still curious if there are there any other usage differences between the two? Is 究竟 only used in examples that are relatively “夸张”

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> E.g. 你究竟为什么要离开我。
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Answer: 
1) "究竟" is more formal than "到底". In everyday spoken Chinese, "究竟" is rarely used. It is used almost only in drama and written Chinese.

2) Well, I would say that the magnitude of "究竟" is equal to that of "到底". They are all equivalent to "on the earth".
There's another meaning for [到底](https://youdao.com/w/%E5%88%B0%E5%BA%95), i.e., "to the end", while [究竟](https://youdao.com/w/%E7%A9%B6%E7%AB%9F) does not have this meaning. E.g.:

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> We must fight on until the end.  
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> 我们必须继续斗争**到底**。
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This is described in more detail in the textbook *标准教程HSK4下* on pages 132-133, which says:

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> Similarity: Both can be used as adverbs in interrogative sentences of sentences with an interrogative word to indicate inquiry and strengthen the interrogative mood. Both can only be put before the subject if the subject is an interrogative pronoun.
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> > 无论做什么事情，只有试过才知道**究竟/到底**能不能成功。  
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> > 人的一生中，**究竟**什么是最重要的？
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> Differences: "到底" can be used as a verb, meaning "till the end", while "究竟" has no such usage.
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> > 你耐心点儿！这个电影得看到**到底**，才能知道那件事情的原因。  
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> > 我们已经做了这么多努力了，一定要把这个计划坚持**到底**，现在放弃太可惜了。
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It also describes 究竟 as follows:

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> ... It is often used in written Chinese. If the subject of the sentence is an interrogative pronoun, "究竟" can only be put before it.
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The *Chinese Grammar Wiki* further highlights how 究竟 is more formal than 到底:

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> When someone asks you "what on earth are you doing?," "究竟 (jiūjìng)" is used by the speaker to intensify the question. In this case, 究竟 is similar to 到底. ... Note that 究竟 is more formal than 到底.  
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> [Expressing "in the end" with "jiujing"](https://resources.allsetlearning.com/chinese/grammar/Expressing_%22in_the_end%22_with_%22jiujing%22)
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