Question

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Answer 1

I have no idea where to start.

Answer 2

derivative of dx/dy can be d^x/dy^2

i don't understand the question clearly, could you please take a screenshot of question and attach if psble ?

Answer 3

I just dont understand what the question wants from me.. its not like you can user linear interpolation so does it just want me to differentiate then plug in 0.5?

Answer 4

actually it would be easier to do dx/dy = 1 / (dy/dx )

Answer 5

1/f'(0.5) ?

Answer 6

but thats not an approximation

Answer 7

i also find the wording strange in the question. what topic is this

Answer 8

numerical approximation, we have been studying things like interpolation and Taylor series

Answer 9

ok, do you have a similar question

Answer 10

is this the first question of its kind, that you have seen

Answer 11

Not really, the next question was simple, it used interpolation to show approximations for the function f(x) = x^2 when x0 = 1, and we had to show how the error approximation is dependant upon the difference between x and x0

Answer 12

ok then it may involve interpolation

Answer 13

but I have no starting x for this

Answer 14

xo = .5 ?

Answer 15

but how can we do y = f(x0) + f'(x0) * (X - x0) when we dont have an X?

Answer 16

maybe we should use 0 then,

Answer 17

it looks like you are doing linear interpolation there

Answer 18

y = f(0) + f'(0) * (x-0)

Answer 19

f(0) = 2.718

Answer 20

ok then we need the taylor series here

Answer 21

right f(0) = e

Answer 22

woops
y = f(0) + f ' (0) * (x-0) + f ' ' (0) ( x - 0)^2 / 2

Answer 23

i take back what i said

Answer 24

ok i think i see what they want, first find dx/dy , then approximate it numerically (using linear or taylor series)

Answer 25

so the first thing you need to do is find dx/dy

Answer 26

dx/dy = 1/ f(x) * ((exp(x) +1)cos(x)-exp(x)sin(x)) according to wolfram

Answer 27

can you post the link for that, wolfram

Answer 28

i can't seem to get the same answer

Answer 29

just did the 1/dy/dx

Answer 30

http://www.wolframalpha.com/input/?i=dy%2Fdx+exp%28sin%28x%29+%2B+cos%28x%29exp%28x%29%29

Answer 31

ok that looks good

Answer 32

now we need one more fact

Answer 33

what X are we trying to approximate for?