# Tutor profile: Sunny L.

## Questions

### Subject: Mandarin

Based on the following conversation, did Xiao Ming (小明） answer the exam question correctly? 小红: 考试完了以后你对答案了吗？ 小明：对了 小红：做对了吗？ 小明：没对

The short answer is that he did not. Let's dissect the conversation and point out common areas for confusion: Xiao hong asked: Did you check your answers (with someone else / answer sheet) after the exam? [Here "对“ is a verb and means "cross check" (the part about correct answer sheet is implied)] Xiao ming answered: Yes I did (here “对” means the same as above - meaning that he did check the answers. Here the subject is omitted, and if we write out the full sentence it would be "我对答案了“） Xiao hong asked: Did you get it (the answer) right? (Here ”对“ means "correct” as an adjective - xiao hong is asking if Xiao ming got the question right) Xiao ming: No it was wrong ("对“ here also means "correct", ”没“ means "not", thus he was saying "not correct")

### Subject: Calculus

Prove that $$\sqrt{x}$$ on [0, $$inf$$) is uni-formally continuous

To show the above statement is true, we need to show for a given ϵ>0 there exists a δ>0 such that for all non negative x1, x2∈R we have |x1−x2|<δ implies that |f(x1)−f(x2)|<ϵ. (note that this also implies such function is lipschitz - we can try to prove this as a separate statement in a different session). Let ϵ>0 (this needs to be an arbitrary positive real number, note the statement "for a given", thus our delta value needs to satisfy the condition for any epsilon). Pick δ=ϵ^2 (since epsilon is already set, delta value can be set this one, this is allowed). Then for any non negative x, y, if $$ \lvert x - y \rvert<δ $$, we have $$\lvert \sqrt(x) - \sqrt(y)\rvert^2 \leq \lvert \sqrt(x) - \sqrt(y)\rvert \lvert \sqrt(x) +\sqrt(y)\rvert = \lvert x - y\rvert <δ= ϵ^2$$ Then: $$ \lvert \sqrt(x) - \sqrt(y)\rvert < ϵ $$

### Subject: Economics

Why is the female employment rate in rural India stagnant or declining despite the economic growth in the past two decades?

It is a complicated question: one possible reason is that the relationship between labor force participation and economic growth is shaped like a "U - curve" -- when an economy is highly unproductive, households had no choice but to send everyone, including women, to the workforce. As this originally under developed economy keeps growing (but before it reaches the same productivity as a developed country), and as women get more educated, they think the return to human capital is higher if they stay at home and take care of their children. As more educated women marry more educated husbands, the latter may encourage their wives to stay at home for cultural reasons.

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