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Prove that the product of two even or tw...

Prove that the product of two even or two odd functions is an even function, whereas the product of an even and an odd function is an odd function.

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Prove that the product of two odd functions is an even function while their sum is an odd function.

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Odd & Even Function

IA MARON-INTRODUCTION OF MATHEMATICAL ANALYSIS-Additional Problems
  1. An isosceles triangle of a given perimeter 2p=12 revolves about its ba...

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  2. Investigating the domain of definition of functions. (a) Solve the i...

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  3. Prove that the product of two even or two odd functions is an even fun...

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  4. Prove that if the domain of definition of the function f(x) is symmetr...

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  5. Prove that any function f(x) defined in a symmetrical interval (-l, l)...

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  6. Extend the function f(x)=x^2 + x defined on the interval (0,3) onto th...

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  7. Prove theat the Drichlet function lambda(x) is a periodic one but has ...

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  8. Prove that if the function f(x)=sin x+cos a x is a periodic, than a is...

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  9. Prove that the sum of two functions increasing on a certain open inter...

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  10. Give an examole of non-monotonic functions that has an inverse.

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  11. Determine the inverse function and its domain of definition, if (a) y=...

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  12. Show that the equation x^(2)+2x+1+sqrtx has no real roots.

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  13. Prove that if the graph of the function y=f(x), defined throughout the...

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  14. Let the sequence xn converge and the sequence yn diverge. What can be ...

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  15. Let the sequences xn and yn diverge. Can one assert that the sequences...

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  16. Let alpha(n) be an interior angle of a regular n-gon (n=3,4,...). Writ...

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  17. Prove that from underset(n to oo) xn=a a it follows that underset(n t...

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  18. Prove that if the sequence {an//bn} {bn gt 0} is monotonic, then the s...

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  19. Prove the existence of limits of the following sequences and find them...

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  20. Prove that if the function f(x): (1) is defined and monotonic on the i...

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