Tangents & Normals to Logs (1 Viewer)

[sando]

can someone please just quickly tell me what--- (e^-x + 1 )^2 is ????

thanks

 

[SoulSearcher]

e^-2x + 2e^-x + 1, I think.

 

[Riviet]

e^-2x + 2e^-x + 1, I think.

That's correct.

 

[sando]

thanks 4 that but hmm... thats what i got.... must be a mistake in my other working out... h8 when that happens lol

can u plz give this question a go with working out....

Find the volume of the solid formed when the curve y = e^-x + 1 is rotated about the x-axis from x=1 and x=2, correct to 1.d.p

 

[Riviet]

V=

2
pi∫e^-2x+2e^-x+1 dx =
1

pi[-e^-2x/2 - 2e^-x + x] ²₁

= pi[(-e^-4/2 - 2e^-2 + 2) - (e^-2/2 - 2e^-1 + 1)]

=4.8 (1dp)

 

[sando]

thanks riviet.... i forgot the minus sign in front of the first e.... arghhhh

 

[Riviet]

Yeah, try to be very careful in your working, one little error and your final answer will be wrong.

 

[pLuvia]

But even if you think it's wrong still try and get an answer since working out will sometimes give you marks

 

[sando]

Having trouble with differentiating logs:

1) log_e (log_ex)

 

[webby234]

d/dx ln[f(x)] = f'(x)/f(x)

so d/dx [ln(lnx)]

= (1/x)/lnx

= 1/(xlnx)

 

[sando]

thnx mate

 

[sando]

Find the point of inflexion on the curve y = xlog_ex - x²

 

[pLuvia]

y=xlnx-x²
y'=(lnx+1)-2x
y''=(1/x)-2=0
Point of Infexion when y''=0
(1/x)-2=0
(1-2x)/x=0 [x*0]
1-2x=0
x=1/2
y=1/2ln(1/2)-1/4
POI=(1/2,[1/2ln(1/2)-1/4])

Then test for change in concavity

 

[sando]

sweet

 

[sando]

Problem involving Volume:

Find the volume of the solid formed when the curve y = 2/√(2x-1) is rotated about the x-axis from x = 1 to x = 5, giving in exact form

Thanks

 

[Trev]

int. 2.(2x-1)^-1/2 dx {1->5}
2.2.(1/2).[2x-1]^1/2 {1->5} etc.

 

[SoulSearcher]

y = 2/√(2x-1)
y² = 4/(2x-1)
therefore volume is
pi ₁∫⁵ 4/(2x-1) dx = [ 2ln(2x-1) ]⁵₁
= pi (2 ln(9) - 2 ln(1))
= pi (2 ln(3²) - 0)
= 4pi ln3 units cubed

 

[SoulSearcher]

int. 2.(2x-1)^-1/2 dx {1->5}
2.2.(1/2).[2x-1]^1/2 {1->5} etc.

That would be right if it was asking for area, not volume.

 

[sando]

nevermind...
i made mistake in working out, rather than completer misunderstanding lol lol

 

[sando]

never mind... i found answer...

2pi (in9) units³