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March 29, 2024, 06:28:33 am

Author Topic: Mathematics Question Thread  (Read 1296857 times)  Share 

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RuiAce

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Re: Mathematics Question Thread
« Reply #285 on: August 06, 2016, 08:48:19 am »
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If they a function is monotonic increasing does that mean f(x)>0 or f(x)>=0? If so why, I can't seem to distinguish between the two
f'(x)≥0

Don't forget the dash

A stationary point doesn't necessarily impede it being "monotonic" increasing. f(x)>0 still satisfies monotonic increasing but more specifically it means strictly increasing.
« Last Edit: August 06, 2016, 08:49:53 am by RuiAce »

conic curve

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Re: Mathematics Question Thread
« Reply #286 on: August 06, 2016, 05:03:59 pm »
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f'(x)≥0

Don't forget the dash

A stationary point doesn't necessarily impede it being "monotonic" increasing. f(x)>0 still satisfies monotonic increasing but more specifically it means strictly increasing.

I don't get it. Could you please elaborate on f'(x)>0 and f'(x)>=0 (and try to give me examples)

Thanks

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #287 on: August 06, 2016, 05:11:51 pm »
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I don't get it. Could you please elaborate on f'(x)>0 and f'(x)>=0 (and try to give me examples)

Thanks


conic curve

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Re: Mathematics Question Thread
« Reply #288 on: August 06, 2016, 05:13:15 pm »
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Finally this cleared things up for me  ;D

Thanks

When would you actually use it (with an example question)

RuiAce

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Re: Mathematics Question Thread
« Reply #289 on: August 06, 2016, 05:14:28 pm »
+1
I don't get it. Could you please elaborate on f'(x)>0 and f'(x)>=0 (and try to give me examples)

Thanks





Further reading: Wikipedia

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Edited on:

« Last Edit: August 06, 2016, 05:20:11 pm by RuiAce »

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #290 on: August 06, 2016, 05:16:35 pm »
+1
Finally this cleared things up for me  ;D

Thanks

When would you actually use it (with an example question)

Check that post again, I made a slight error, fixed now :) (and Rui goes into more detail if it helps). No problem, to be honest it is a tiny thing, it is unlikely to be pressed hard. If you are asked whether a function is monotonic increasing (they probably wouldn't use this language in 2U tbh), then just remember the dash, that's all ;D

olivercutbill

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Re: Mathematics Question Thread
« Reply #291 on: August 07, 2016, 12:50:41 pm »
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Can someone explain 'b)' and 'c)'?

Thank you!
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zsteve

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Re: Mathematics Question Thread
« Reply #292 on: August 07, 2016, 01:38:07 pm »
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Can someone explain 'b)' and 'c)'?

Thank you!

For (b), you'll have to differentiate for the velocity as a function of time. Then solve for zeros.
For (c), you'll have to use a definite integral. Assuming $t$ can only be positive, $x$ is defined over the interval \([0, 7]\), so 'altogether' means from t=0 to t=7.

These are standard procedures in kinematics :)
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RuiAce

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Re: Mathematics Question Thread
« Reply #293 on: August 07, 2016, 01:41:27 pm »
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Can someone explain 'b)' and 'c)'?

Thank you!






For (b), you'll have to differentiate for the velocity as a function of time. Then solve for zeros.
For (c), you'll have to use a definite integral. Assuming $t$ can only be positive, $x$ is defined over the interval \([0, 7]\), so 'altogether' means from t=0 to t=7.

These are standard procedures in kinematics :)
The statement is true but I disagree with its suitability. Integrating that velocity function is way outside 2U level. Actually it's fine, forgot that we had the antiderivative given, sorry :)

But we don't need to. We can just rely on x(t).
« Last Edit: August 07, 2016, 01:47:54 pm by RuiAce »

jakesilove

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Re: Mathematics Question Thread
« Reply #294 on: August 07, 2016, 01:45:27 pm »
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Can someone explain 'b)' and 'c)'?

Thank you!

Dammit guys, I was just posting a solution. But yeah got to the same thing; I better pick up my game
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olivercutbill

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Re: Mathematics Question Thread
« Reply #295 on: August 07, 2016, 07:32:26 pm »
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I won't quote everything but cheers guys!

Problem was I forgot to use the product rule in part b). Classic error.
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conic curve

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Re: Mathematics Question Thread
« Reply #296 on: August 08, 2016, 10:51:04 am »
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Need help with this Q

jakesilove

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Re: Mathematics Question Thread
« Reply #297 on: August 08, 2016, 11:02:02 am »
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Need help with this Q

Let's start by simplifying some stuff



By difference of two squares. But, p+q=1, so





Now, let's use sum of two cubes


As p+q=1



As required
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conic curve

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Re: Mathematics Question Thread
« Reply #298 on: August 08, 2016, 01:04:27 pm »
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Let's start by simplifying some stuff



By difference of two squares. But, p+q=1, so





Now, let's use sum of two cubes


As p+q=1



As required

Thanks Jake

How would I do question iii and iv

RuiAce

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Re: Mathematics Question Thread
« Reply #299 on: August 08, 2016, 01:08:11 pm »
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Thanks Jake

How would I do question iii and iv