Show the inequality $ sec x ge 1+ (x ^ 2/2) $

Test inequality

$ sec (x) ge 1+ (x ^ 2/2) $

How do I distinguish the meaning of the SQL Performance Counters as Transactions / sec. And Errors / sec? [duplicate]

This question already has an answer here:

  • Batch requests / sec. Reported by the DMV millions of times larger than the Activity Monitor

    3 answers

I have been storing a lot of SQL performance counters in the last 10 days or so. I am looking to make a dashboard in the health of the server with this data. My question arises when I start looking at my meters that involve a "metric" / sec (Transactions / sec., Errors / sec., Etc.).

According to my understanding, the name implies that these counters should show me an aggregated statistic according to the time consulted on how many errors or transactions occur per second. Everything I have read online about these performance counters seems to affirm this description. However, you will notice in the image below that the number is high (423,683 transactions / sec), and it grows significantly every day. It seems to me that you are adding the transaction counter per second to the previous sums, if that makes sense. Is this the expected behavior? If so, to get the value I'm looking for, do I need to subtract the days to get the Transactions / sec for that day?

Transactions / sec For a single database registered for many days.

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Trigonometric equation including sec

What are the values ​​of x in degrees when:
sec ^ 2 (x) -2 sqrt {2} sec (x) + 2 = 0

I think you should use derivatives of $ sec (x) $ but I'm fighting.
Any help would be appreciated.