Prove disprove that for $a$, $b$, $c$, $d$ are real numbers

Question

Can any one solve the following two for me:

1- Let $a$, $b$, $c$ and $d$ be real numbers satisfying $a>b$ and $c>d$. Does this imply that $ac>bd$? Prove or disprove.

2- From the analysis concepts find $$ \lim_{n\to\infty}\frac{3^n+n^3}{(2n)^2+2^{2n}}\,. $$

I really appreciate your effort.

score 2 · Answer 1 · answered Apr 12 '13 at 07:25

2

Hint: Rewrite $2^{2n}$ as $4^n$. Then divide top and bottom by $4^n$. Then take the limit. You will need to know that in the long run an exponential grows far faster than any polynomial.

For the first problem, note that it says real number. You should be able to find an example where the result fails. Think negative!

answered Apr 12 '13 at 07:25

André Nicolas

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could you be more precious, please? I mean what to divide by 4^n? what about 3^n and n^3? – LoveMath Apr 12 '13 at 07:37

score 1 · Answer 2 · answered Apr 12 '13 at 07:25

1

Let $a=c=1$, $b=d=-2$. Clearly $a>b$ and $c>d$ but $ac < bd$.

answered Apr 12 '13 at 07:25

Prove disprove that for $a$, $b$, $c$, $d$ are real numbers

2 Answers2

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