Year 12s: what will be the first way you research your future options? >>

Please help with these questions-limits etc.

betapro

I've attached the questions, thank you so much in advance.

asdfadsafasdf.pdf88.2KB

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Reply 1

Thisguy11

Could you start the problems yourself?
let us know what you have tried, im sure people will want to help, but few would be okay with doing it for you

Reply 2

betapro

I require some assistance with 2,3,4. with 3 i think it is either b or f or both not sure though. Thanks

Reply 3

betapro

For question 3- For (b) i can show its less than for any n but not equal so not sure and same for (f) can show its greater than but not the equal part.

Reply 4

EricPiphany

Original post by betapro

For question 3- For (b) i can show its less than for any n but not equal so not sure and same for (f) can show its greater than but not the equal part.

So what did you do for 3 (b)?

Reply 5

MathMoFarah

Original post by betapro

For question 3- For (b) i can show its less than for any n but not equal so not sure and same for (f) can show its greater than but not the equal part.

b and f are correct and the answer is 4 - the 'or equal to' part is unnecessary but used in all of them so you can ignore it - the statements are still true

what have you tried for 2&4?

Reply 6

betapro

I just tried tons of numbers for small n and large and always worked but cant find an n that it is equal or a way of showing mathematically that they are

Reply 7

EricPiphany

Original post by betapro

I just tried tons of numbers for small n and large and always worked but cant find an n that it is equal or a way of showing mathematically that they are

Does this make any sense to you?

\displaystyle \frac{n-1}{n^2+1} \le \frac{n}{n^2+1}

Reply 8

betapro

Yes, where from there?

Reply 9

betapro

oh and then u get rid of 1 and then get 1/n

Reply 10

betapro

So then B is correct right? what about f

Reply 11

EricPiphany

Original post by betapro

So then B is correct right? what about f

Difference of squares?

Reply 12

betapro

Original post by MathMoFarah

b and f are correct and the answer is 4 - the 'or equal to' part is unnecessary but used in all of them so you can ignore it - the statements are still true

what have you tried for 2&4?

Yes for 2 i got 6) so L=1 and not a clue how to do 4 :biggrin:

Reply 13

MathMoFarah

Original post by betapro

Yes for 2 i got 6) so L=1 and not a clue how to do 4 :biggrin:

your 2 is right

you have to manipulate things for 6 until you get something that HAS to follow the inequality
i.e. a higher denominator and lower numerator always guarantees a lower number

Reply 14

betapro

Original post by MathMoFarah

your 2 is right

you have to manipulate things for 6 until you get something that HAS to follow the inequality
i.e. a higher denominator and lower numerator always guarantees a lower number