From the revision session today…
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Y13 C3 Differentiation Revision Questions18 comments to Y13 C3 Differentiation Revision Questions |
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For a differentiation question (not on these sheets):
f(x) = 4tanxtan5x
for f’(x) I get -> 4(sec^2)x tan5x + 20tanx(sec^2)5x
(where none of the xs are multiplacation, they’re all xs)
But the answer is given as f’(x) = 40tan5x(sec^2)5x
I guess that (sec^2)x = (tan^2)x + 1 is used in this – but I can’t quite work it through for myself…
I’m also a bit confused on questions like:
e^x + 3e^-x = 4
where you have to add powers -> should I turn the 3e^-x into 3 (e^1 / e^x) or 3 (e^-1 (multiplied by) e^x) ??
Hope that made sense with all the powers,
Thank you
Grace.
Hi Grace,
For the exponential ones like that, I multiply throughout by e^x and then get a quadratic in e^x.
Will look at the tan one for you and come back.
JT
Grace,
Where is that differentiation question from?
JT
Thanks for that advice about the eponentials.
The differentiation question is from the “Revise for C3″ book – from the same publishers as the old style textbooks. It’s Example 5 of Chapter 8 – but even still I don’t understand their method of working out.
Is there some way I could write it clearer?
Grace
Hi Grace,
I haven’t managed to get what they got!!
What’s the next line after the one you typed out?
JT
Uhoh.
I have just realised that the question asks you to differentiate 4(tan^2)5x… so not 4tanxtan5x at all…
Sorry for that waste of your time, Mrs Tibble!
Read the question Grace!
lol!
hello, do know where I could get the janurary 2009 c2 mark scheme please, thanxxx.
Bernice,
Check your school e-mail.
JT
Hi please may i have some help with this question:
Use the iterative formula
xn+1 = 2 + (1/xn^2 + 1)
with a suitable starting value to find the root of the equation f(x) = 0 correct to 3 significant figures and justify the accuracy of your answer.
I understand how to work it out, Im just not sure on how to work out a ‘suitable starting value’. The mark scheme recommends it to be 3 but i dont know why this is.
Thanks
Jacynth
Also, why does logx = lnx/ln10 please?
Hi Jacynth,
2nd question first: because ‘log’ is the shorthand for logs to base 10, whereas ‘ln’ is to base e; it’s the change of base formula.
JT
Hi Jacynth,
Did you have to show that there was a root in the interval 2-3 or 3-4 as the 1st part of the question?
Also, is it (1/x^2) + 1 or is the denominator (x^2 + 1)
Thank you! i understand now!
no it just wanted you to find the root with the iterative formula. the denominator is (x^2 + 1). it wants you to find a suitable starting value but im not sure how to work that out
also for Mr Brewin: Sir i’ve mislaid the sheet you wrote us out on all the different values we need to know for trig. would you be able to send me another copy please as i am frantically trying to find it but i cant :/
Thanks
Jacynth
Hi Jacynth,
Find 2 consecutive integers which give a sign change for the function. Start your iteration with one of them. If your first iteration makes the value worse – ie you move away from the interval, then start again with the other one.
JT
Great thankyou!
Jacynth
Just to jump in here, Jas, You can work out all the trig angles by drawing the three triangles (If I think you’re talking about the sheet I’m thinking about)
The first triangle is an equilateral split down the middle (so the sides are 2, 1 and root3 – it gives the 60 and 30 angles)
The second is a 3,4,5 triangle – that gives you any angle
The third is an isos – two sides of 1 and the 3rd root (angle 45)
Is that the one??
xxx
ooh typo
(the third triangle has two sides of 1 and the 3rd side is root2)