What is .. 30% of .. is 60 ?

1 answer:

8 0

So question is 'what is x. 30% of x is 60'

remember that percent means parts out of 100 so therefor
30%=30/100=3/10
so the question is
3/10 of x is 60
'of' in math means multiply
3/10 times x=60
3x/10=60
mulitply both sides by 10 to get rid of fraction
3x=600
divide both sides by 3
x=200

.. is 200

the number is 200

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Exercise 2.2.5. Let [[x]] be the greatest integer less than or equal to x. For example, [[π]] = 3 and [[3]] = 3. For each sequen

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Answer:

a) $\lim_{n\rightarrow \infty}a_n=0$

b) The limit is [[4/3]]=1, that is, $\lim_{n\rightarrow \infty}a_n=1$

Step-by-step explanation:

The definition of the limit of a sequence (an) is as follows:

$\lim_{n\rightarrow \infty}a_n=L$ (the sequence (an) converges to L) means that given $\epsilon>0$ , there exists some natural number N such that if n≥N, then $|a_n-L|$

We will use that [[x]] is a increasing function. That is, if x≤y then [[x]]≤[[y]]

a) For all $\epsilon>0$ , take N≥6. Then 1/N ≤1/6 and 5/N ≤ 5/6 < 1. We have that 0<5/N<1, therefore [[5/N]]=0 (0 is the biggest integer less than or equal than x, for any x on the interval 0<x<1)

For n≥N, we have that 1/n ≤ 1/N, hence 0< 5/n ≤ 5/N < 1 . As we discussed above, [[5/n]]=0. Then |a_n|=0, therefore $|a_n-0|=|a_n|=0$