证明 Big-Theta 表示法
你好，我已经尽力理解 big-theta，现在我得到了 Big-Oh 和 Big-Omega 证明的主要概念，但我找不到与我的练习接近的示例，因为我无法做到 一点
证明：通过展示证人证明 4n^2 + 4n = Big-Theta(2n^2 + 32n)
我知道我必须为 Big-Oh 和 Big-Omega 证明这 才能证明 Big- Theta，但我不知道如何开始。我的意思是右边的方程让我感到困惑。
Hello I've tried my best to understand big-theta and now I get the main conception of the proofs for Big-Oh and Big-Omega but i couldn't find and example that is close to my excercise, because i cant do the proof for that one:
Prove, by exhibiting witnesses, that 4n^2 + 4n = Big-Theta(2n^2 + 32n)
I know that i have to prove it for Big-Oh and Big-Omega in order to prove Big-Theta, but i have no idea how to start. I mean the equation on the right side confuses me.
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根据big-theta的定义，你需要证明存在两个常数，k1和k2，这样对于所有足够大的 n 值，
（由于您的函数对于正 n 都是正的，因此您可以删除绝对值。）只需证明每个不等式可以单独满足即可。
By the definition of big-theta, you need to show that there exist two constants, k1 and k2, such that for all sufficiently large values of n,
(Since your functions are all positive for positive n, you can drop the absolute values.) Just show that each inequality can be satisfied separately and you're done.