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SUKBarracuda
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#1
Report Thread starter 15 years ago
#1
Can anyone help me with these practice questions?

1)

Given that y = x^(sinhx)

prove:

y.d²y/dx² - (dy/dx)² = y² / x


2)

Given that sinhx = tant 0 < tant t < (pi)/2

Prove:

i) tanhx = sint

ii) e^x = sect + tant


Cheers. I could do them yesterday and now i cant and can't find my notes. I hope i don't forget stuff in the exam. :rolleyes:
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theoffender
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#2
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What does ^ mean? And what exam board are you doing? Because I've never seen questions lke that in my life and I'm doing OCR P5 on monday!
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acidbubble
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it means to the power of, 2^2 = 4
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SUKBarracuda
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well i'm doing edexcel, but hyperbolics and differentiation/integrastion are both on the ocr p5 syllabus, so it should resemble your work...
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queen-of-pain
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I've done a question like the second one. Have you tried squaring it and then using identities? Although the question i did was prove that coshx = sect and the second part is just using the relationship you proved in the first part.

As for the first question I'd suggest taking logs and then using implicit differentiation and the product rule.
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mikesgt2
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The first question is a mistake, I have come across it on another forum on which somebody said they had rung up Heinmann who confirmed the question was wrong. It should be y=x^x, rather than y=x^(sinhx).
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infekt
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(Original post by mikesgt2)
The first question is a mistake, I have come across it on another forum on which somebody said they had rung up Heinmann who confirmed the question was wrong. It should be y=x^x, rather than y=x^(sinhx).
yup ... my maths teacher said tht too ... the answer at the backis wat it should b for x^x
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qqqwwweee
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(Original post by SUKBarracuda)

2)

Given that sinhx = tant 0 < tant t < (pi)/2

Prove:

i) tanhx = sint

ii) e^x = sect + tant
i)
tanhx = sinhx/coshx = tant/coshx

and cosh^2 x - sinh^2 x = 1
so coshx = root(1 + sinh^2 x) = root(1+tan^2 t) = root(sec^2 t) = sect

so tanhx = sinhx/coshx = tant/coshx = tant/sect
rearrange it and you ll get sint

ii)from above, coshx = sect
so sect + tant = coshx + sinhx = e^x
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