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[數學,M1&M2] HKDSE Mathematics Question Review 2020-07-26



HKDSE Mathematics Question Review 2020-07-26

[隱藏]
1. Show that y=x^0.2 is multivalued.

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solution:


y^5=x
x is a function of y, but not vise versa.

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2. Given abcde=i
show that a, b, c, d, e cannot be expressed as elementary functions.




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Solution:


i = i^5 = i^9 = ...
implies
i^-3 = i = i^5 = ...
and so on due to periodicity.
Since i itself is multivalued,
abcde cannot be commutative.

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[隱藏]
3. Explain why cross product is anticlockwise.

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Solution:


By definition of Cartesian coordinates, x to y is anticlockwise. so to make y to z anticlockwise, x to z must also be anticlockwise. That's the origin of right hand grip rule.

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