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# fp2 maclaurin watch

1. so how do you expand ln(2 + 3x), i can clearly see you can split it like
ln( 2(1+1.5x) ) = ln2 + ln(1+ 1.5x). but then what?

do i just dip the 1.5x in the formula? it doesnt make sense to me.......
2. (Original post by cooldudeman)
so how do you expand ln(2 + 3x), i can clearly see you can split it like
ln( 2(1+1.5x) ) = ln2 + ln(1+ 1.5x). but then what?

do i just dip the 1.5x in the formula? it doesnt make sense to me.......
Dip? If you mean replace x in your standard expansion with 1.5x then yes.
3. (Original post by Mr M)
Dip? If you mean replace x in your standard expansion with 1.5x then yes.
that simple.. nice.
4. (Original post by cooldudeman)
so how do you expand ln(2 + 3x), i can clearly see you can split it like
ln( 2(1+1.5x) ) = ln2 + ln(1+ 1.5x). but then what?

do i just dip the 1.5x in the formula? it doesnt make sense to me.......

Use here the formula for infinite geometric series

Whit that
Integrating pointwise you will get the series
5. (Original post by ztibor)

Use here the formula for infinite geometric series

Whit that
Integrating pointwise you will get the series
yeah i kinda see it now. thanks.

could you or anyone else help with differential equations using Taylors series, its the last part in the book with this topic. i don't understand it at all and i have done 1st and 2nd diff orders.

can you just go through this question
d2y/dx2 = y - sinx, use the taylor method to find a series solution, until x^3 given that when x=0, y=1 and dy/dx = 2
6. (Original post by cooldudeman)
yeah i kinda see it now. thanks.

could you or anyone else help with differential equations using Taylors series, its the last part in the book with this topic. i don't understand it at all and i have done 1st and 2nd diff orders.

can you just go through this question
d2y/dx2 = y - sinx, use the taylor method to find a series solution, until x^3 given that when x=0, y=1 and dy/dx = 2
Start the homogeneous part: y"-y=0
From this you wil get the general solution
For particular y_p use the variation of parameters c1(x) and c2(x)
You will get for c1(x) and c2(x) some sinx*e^x type integral
Write the solution of them with Taylor series for e^x and sinx, cosx
7. (Original post by cooldudeman)
yeah i kinda see it now. thanks.

could you or anyone else help with differential equations using Taylors series, its the last part in the book with this topic. i don't understand it at all and i have done 1st and 2nd diff orders.

can you just go through this question
d2y/dx2 = y - sinx, use the taylor method to find a series solution, until x^3 given that when x=0, y=1 and dy/dx = 2
Arrange to y"-y=-sinx

Assuming that

shifting n by 2
Substituting into the original equation

arranging

Equating the coeffitients of like terms

This is a recurremve relation and you van get a0 and a1 from the
initial conditions, then a2 and so the first 3 terms of y.
Good work
8. (Original post by ztibor)
Arrange to y"-y=-sinx

Assuming that

shifting n by 2
Substituting into the original equation

arranging

Equating the coeffitients of like terms

This is a recurremve relation and you van get a0 and a1 from the
initial conditions, then a2 and so the first 3 terms of y.
Good work
ok thank you for all your help. appreciate it.

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