help with Series/trigonometry question and differentiating an equation with logs?? (1 Viewer)

kiniki

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ok so im doing some past HSC papers for 2U maths and i came across these two questions and they totally stumped me, i looked at them and didn't even know where to start!!

first one is

Q1 a) Consider the geometric series 1 - tan^2 θ + tan^4 θ ...

i) when the limiting sums exists, find its value in simplest form

(ok so the limiting sum formula is S∞ = a/1-r yeah? a = 1 and how the fuck do i find the ratio ??? this question totally throws me and i know that its heaps similiar to what alot of questions will be like in the actual HSC so im stressing! is the ratio between the thingies, tan^2? or does it have something to do with trig identities and the ASTC?)

ii) for what values of θ in the interval -π/2 < θ < π/2 does the limiting sum of the series exist?

(so it does have something to do with ASTC?) ((WTF is this question??))

:confused:




and the next question

Q2 a) Consider the function f(x) = loge x/x, for x > 0

i) show that the graph y = f(x) has a stationary point of x=e

(i started off with the quotient rule but HOW DO I DIFFERENTIATE A LOG? is it; y = loge x... y' = 1/x ? is that it? ive done nearly shit all on log laws :S)
(i don't get the wording of this question? not how to do the question but huh wait stop wut y=f(x)? am i making some really elementary maths error here?)
(x=e?? ive only dont stationary points where x = a number... e??? what is e?)

ii) dw about (ii)

iii) use the fact that the maximum value of f(x) occurs at x=e to deduce that e^x > (greater than or equal to) x^e for all x > 0

(im completely lost the moment it gets to deduce that rarara. even if i knew the turning points in (i) and graphs whatvs i would have nooo idea with this question)



And i went to my teacher about this today, and shes like dw i only gave you this to show you how hard its going to be.

how hard its going to be in 9 months??? i dont know how to do half the questions in these hsc papers because i havent learnt them yet ARRGHHH what the hell??? and im going to be doing the HSC for it in 9 months? is she crazy!


help :(
 

cutemouse

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Re: help with Series/trigonometry question and differentiating an equation with logs?

ok so im doing some past HSC papers for 2U maths and i came across these two questions and they totally stumped me, i looked at them and didn't even know where to start!!

first one is

Q1 a) Consider the geometric series 1 - tan^2 θ + tan^4 θ ...

i) when the limiting sums exists, find its value in simplest form

(ok so the limiting sum formula is S∞ = a/1-r yeah? a = 1 and how the fuck do i find the ratio ??? this question totally throws me and i know that its heaps similiar to what alot of questions will be like in the actual HSC so im stressing! is the ratio between the thingies, tan^2? or does it have something to do with trig identities and the ASTC?)

ii) for what values of θ in the interval -π/2 < θ < π/2 does the limiting sum of the series exist?

(so it does have something to do with ASTC?) ((WTF is this question??))

:confused:
You need to cover trig functions to fully understand this. It's basically to do with the domain and range of the tan function.

If you still want help, ask I can be bothered to answer at the moment...



and the next question

Q2 a) Consider the function f(x) = loge x/x, for x > 0

i) show that the graph y = f(x) has a stationary point of x=e

(i started off with the quotient rule but HOW DO I DIFFERENTIATE A LOG? is it; y = loge x... y' = 1/x ? is that it? ive done nearly shit all on log laws :S)
(i don't get the wording of this question? not how to do the question but huh wait stop wut y=f(x)? am i making some really elementary maths error here?)
(x=e?? ive only dont stationary points where x = a number... e??? what is e?)

ii) dw about (ii)

iii) use the fact that the maximum value of f(x) occurs at x=e to deduce that e^x > (greater than or equal to) x^e for all x > 0
Yes d/dx lnx (log to the base e) is 1/x

A stationary point is when dy/dx=0, ie the gradient is zero... Think about it.

Anyway, if you still need help ask.

Thanks
 

independantz

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Re: help with Series/trigonometry question and differentiating an equation with logs?

1)
i)


ii)


2)
i)
 
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