Yeah you can either set x on one side and all the y stuff on the other side and do dx/dy or do implicit differentiation with respect to x, both are basically the same thing.

Reply 184

Don Pedro K.

Original post by 1 8 13 20 42

That does work. Gets you -(gradient of normal)

Yeah lol I just realised I tried to product rule something that doesn't even need product rule xD

Original post by sabahshahed294

By changing everything in terms of x?

Yeah basically I multiplied both sides by (y^2 + lny) so you get x = y(y^2 + lny).

From there, you can find dx/dy and then flip it to find dy/dx :biggrin:

Reply 185

sabahshahed294

Original post by 1 8 13 20 42

Yeah you can either set x on one side and all the y stuff on the other side and do dx/dy or do implicit differentiation with respect to x, both are basically the same thing.

I will try it out. If I see I can't, I'll ask again. Thank you!

Reply 186

sabahshahed294

Original post by Don Pedro K.

Yeah lol I just realised I tried to product rule something that doesn't even need product rule xD

Yeah basically I multiplied both sides by (y^2 + lny) so you get x = y(y^2 + lny).

From there, you can find dx/dy and then flip it to find dy/dx :biggrin:

Thanks!

Reply 187

SaadKaleem

Original post by sabahshahed294

Hi!
Can someone help me out in Q6 here? :smile:

http://www.madasmaths.com/archive/iygb_practice_papers/c3_practice_papers/c3_b.pdf

View at your own risk:

Spoiler

Reply 188

sabahshahed294

Original post by SaadKaleem

View at your own risk:

Spoiler

rofl. Thanks I did it this way :smile:

Your exam is coming up btw. :tongue:

Reply 189

thesuperdark

Hey can someone help me out on question 5c, on this paper.

https://07a69ccf283966549a9350d1a66951a7bc96e2dc.googledrive.com/host/0B1ZiqBksUHNYZ0JQM1NRcmdHdXM/January%202009%20QP%20-%20C3%20Edexcel.pdf

It's to do with ranges and domains, and I put the answer fg > 3, whereas the mark scheme says the answer is fg is greater than or equal to 3 (even though it says in the question that x > 0)

Thanks :smile:

Reply 190

thenextchemist

Original post by thesuperdark

Try drawing it out
That's what I did with this question
You'll see why it's bigger than 3

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Reply 191

NotoriousS

Has anyone got useful tips on how to draw reciprocal graphs? I.e. finding their asymptotes..

E.g. f(x) = (3x+2) / (x-1) ???

Thanks in advance

Reply 192

Supermanxxxxxx

Just got 63/75 on gold paper 4 for edexcel not really sure how to feel about it

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Reply 193

Glavien

Original post by SeanFM

All looks correct :borat:

well done.

Hi, can you check if my domain for part c, f(g(x)) is correct? I done the question again and I am pretty sure I got it wrong and it should actually be

2.5\leq x\leq 3.5

Thanks!

Reply 194

Kevin De Bruyne

Original post by NotoriousS

Has anyone got useful tips on how to draw reciprocal graphs? I.e. finding their asymptotes..

E.g. f(x) = (3x+2) / (x-1) ???

Thanks in advance

Step 1 - look at the fraction and make two inferences.

x=1 is going to be an symptote (as ..../0 is undefined). And the only place where y = 0 is when 3x+2 = 0, hence x = -2/3 is where y =0 (remember that if (a/b) = 0, then a=0).

Then, think about what happens at x = 0 as well. Not completely necessary though.

Finally, look at what happens when x gets to +infinity and -infinity. When x gets large, adding +2 to the numerator or taking away -1 from the denominator becomes insignificant, so you're practically left with 3x/x = 3, which is going to be the limit of y. (you know it's going to be just above 3 though, and never = 3, because the numerator is greater than 3*x and the numerator is less than x. If in doubt, use large numbers like 10000 to see what happens.

For -infinity, the limit is also 3. Similar logic.

Reply 195

Kevin De Bruyne

Original post by Glavien

Hi, can you check if my domain for part c, f(g(x)) is correct? I done the question again and I am pretty sure I got it wrong and it should actually be

2.5\leq x\leq 3.5

Thanks!

Ah yes, sorry! I'm not sure how I missed that :tongue:

but that is correct.

Reply 196

Glavien

Original post by SeanFM

Ah yes, sorry! I'm not sure how I missed that :tongue:

but that is correct.

Thank you!

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Reply 197

imran_

http://www.madasmaths.com/archive/iygb_practice_papers/c3_practice_papers/c3_j.pdf

can someone explain 5b please the range i always seem to get these type of questions wrong

Reply 198

Clovers

Anyone have any tips and general help on finding the domain and range? Especially using graphs. Thanks in advance! :smile:

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Reply 199

Kevin De Bruyne

Original post by Clovers

Anyone have any tips and general help on finding the domain and range? Especially using graphs. Thanks in advance! :smile:

Posted from TSR Mobile

Domain - consider the function and look for x values that will give you 'undefined' values. You can often compare it to normal functions and work from there.
What I mean by that is, for example,

If you had ln(2x+5) then you know that for something simple like lnx, x has to be >0 so you know that in ln(2x+5), 2x+5 > 0 and so x> -5/2.

Also for something like tanf(x) where f(x) is any function of x, f(x) must not be equal to any multiple of pi/2 as it is undefined (easy way to remember - tanx = sinx/cosx, and cosx = 0 when x = pi/2, hence tanx is .../0 = undefined.

And lastly for fractions, you can't divide by 0 - so if you had

\frac{x}{x-3}

for example, then x can take any value but 3.

For the range, it just takes practice. Once you know the domain, it may help to put in numbers close to the domain to see if you can spot the range. If, for example,

\frac{x}{x-3}

had the domain

4 \leq x \leq 7

(for whatever reason, rather than just x = anything but 3) then you could find f(4) = 4 and f(7) = (7/4) and deduce that it is a decreasing function. You could also write the function as

\frac{x-3+3}{x-3} = 1 + \frac{3}{x-3}

to see it more easily.

Also, test out large values of x. If you had

\frac{3x + 1}{x-2}

then as x gets really large (eg 10000, but ideally infinity) y becomes

\frac{3\times 10000 - 1}{10000 - 2}

which is pretty much equal to 3*10000/10000 = 3, and you can tell that it's always going to be greater than 3 as x gets larger as the numerator is slightly greater than 3x, and the numerator is slightly less than 1x so it will always be 3.0000'..12321566 or whatever and you can deduce that y>3.