Foundation of analysis UE Past Papers Questions.


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(1112) Question Category: Mathematical Calculation

If f:mathbb{R} ightarrow mathbb{R} is given by f(x)=3x+7, prove that it is one to one.

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(1113) Question Category: Mathematical Calculation

Let A be a set of non-zero integers and let equiv be the relation on AxA defined by (a,b)equiv(c,d) wherever ad=bc. Prove that equiv is an equivalence relation.

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(1114) Question Category: Mathematical Calculation

Use de Moivre's theorem to express cos4 heta and sin4 heta in terms of powers of cos4 heta and sin4 heta.

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(1115) Question Category: Mathematical Calculation

Find the roots of z^3-z^2 -z-2=0, given that z=2 is a root.

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(1116) Question Category: Mathematical Calculation

Determine if the following sets are bounded or not bounded.

  1. S={{x in mathbb{R}|0leqslant x<1}}
  2. S={{n|ninmathbb{N}}}
  3. S={{frac{1}{n}|ninmathbb{N}}}.

Prove that if the least upper bound of a subset S of Re exists, then it is unique.

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