
[![Harness the power of activerecall](https://flow-prompt-covers.s3.us-west-1.amazonaws.com/icon/vintage/vint_7.png)](https://gptcall.net/chat.html?data=%7B%22contact%22%3A%7B%22id%22%3A%22uiN6qci-vEJESFnkg6Hz1%22%2C%22flow%22%3Atrue%7D%7D)
# Harness the power of activerecall | [Start Chat](https://gptcall.net/chat.html?data=%7B%22contact%22%3A%7B%22id%22%3A%22uiN6qci-vEJESFnkg6Hz1%22%2C%22flow%22%3Atrue%7D%7D)
Challenging Q

# Prompt

```
Provide me with a series of challenging questions or problems related to [topic or skill] to test my understanding and improve long-term retention.
```

## Conversation

**ASSISTANT**: Sure, I'd be happy to provide you with a series of challenging questions or problems related to various topics or skills. Please let me know the specific topic or skill you want to be challenged on, and I'll create a set of questions to test your understanding and improve your long-term retention.
**USER**: Find the limit of (sin(x)-x)/x^3 as x approaches zero.
**ASSISTANT**: To find the limit of (sin(x)-x)/x^3 as x approaches zero, we can use L'Hopital's Rule. 



Taking the derivative of the numerator and denominator separately with respect to x, we get:



lim x→0 [(sin(x)-x)/x^3] = lim x→0 [(cos(x)-1)/3x^2]



Now, plugging in x=0 into this expression will give us an indeterminate form of 0/0. So we can apply L'Hopital's Rule again:



lim x→0 [(cos(x)-1)/3x^2] = lim x→0 [-sin(x)/6x] = lim x→0 [-cos(x)/6] = -1/6



Therefore, the limit of (sin(x)-x)/x^3 as x approaches zero is equal to -1/6.
**USER**: Find the derivative of f(x) = 5x^3 - 2x^2 + 4x - 1.
**ASSISTANT**: To find the derivative of f(x) = 5x^3 - 2x^2 + 4x - 1, we can use the power rule of differentiation. 



The power rule states that if we have a function of the form f(x) = x^n, then its derivative is given by f'(x) = nx^(n-1).



Using this rule and applying it to each term in f(x), we get:



f'(x) = d/dx (5x^3) - d/dx (2x^2) + d/dx (4x) - d/dx (1)

      = 15x^2 - 4x + 4



Therefore, the derivative of f(x) = 5x^3 - 2x^2 + 4x - 1 is f'(x) = 15x^2 - 4x + 4.
**USER**: I encountered a problem of opportunity cost: 1. I chose to study graduate degree and spent 50000 dollars and two years, but there may be better job opportunities in the future. 2. Currently choosing employment, the annual salary is around 250000 RMB, but it may increase to around 400000 RMB in the next two years.
**ASSISTANT**: The problem you are encountering is a classic example of opportunity cost. Opportunity cost refers to the cost of choosing one option over another, in terms of the benefits foregone from not choosing the alternative option.



In your case, there are two options: studying for a graduate degree or choosing employment. By choosing to study for a graduate degree, you are spending 50000 dollars and two years, which means you are giving up the opportunity to earn money during that time. On the other hand, if you choose employment, you will earn an annual salary of around 250000 RMB, but you may miss out on potential higher salaries that could be earned with a graduate degree.



To make the best decision, you need to weigh the costs and benefits of each option. You can calculate the present value of the future earnings from each option and compare them to determine which option has a higher expected value. You can also consider the non-financial benefits of each option, such as personal fulfillment and career growth opportunities.



Ultimately, the decision should be based on your personal goals and circumstances. If you value the long-term benefits of a graduate degree and are willing to invest the time and money required to obtain it, then that may be the best choice for you. However, if you prioritize immediate financial security and job stability, then choosing employment may be the better option.


