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# Tutor profile: Sunny L.

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Sunny L.
Economics PhD Student
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## Questions

### Subject:Mandarin

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Question:

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

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Sunny L.

### Subject:Calculus

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Question:

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

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Sunny L.

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

TutorMe
Question:

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

Inactive
Sunny L.

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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