Question

Use newton's method of approximation to approximate the zero of the function in the indicated interval to six decimal places

f(x) = cos x -x in [0,pi/2]

Our working has to be in radians...but i'm not quite sure how to do that... i know for my x1 it can be pi/4

Answer 1

i would like to know how to do it manually...not on the computer :) thank you :)

Answer 2

f'(x)=-sinx-1

we need to choose an x to start with like x=1/2

\[x_n=x_{n-1}-\frac{f(x_{n-1})}{f'(x_{n-1}}\]
so x_1=1/2
x_2=1/2-f(1/2)/f'(1/2)=.692749953
then
you find x_3 using same process
i do this until my x's start repeating

Answer 3

i think it has to be in radians so i thought we use x=pi/4

Answer 4

x_3=.692749953-f(.692749953)/f'(.692749953)=.7395826723

Answer 5

it is in radians

Answer 6

oh my bad so why u choosed x = 1/2 because the interval is continuous at that point?

Answer 7

i chose 1/2 because it was closer to the x-intercept of the curve
you can do pi/4 if you want

Answer 8

7/10 probably would have been closer

Answer 9

hmm okay let me see how that works out

Answer 10

i thought were focusing on the interval [0,pi/2] and we want a number between that :s lol

Answer 11

we are using the x-intercepts of tangent lines to approximate the x-intercept of the curve

Answer 12

hmm...:S

Answer 13

.5 is between 0 and pi/2

Answer 14

pi/2 is approximately 1.570796 blah blah

Answer 15

pi/2 is .5 no...?

Answer 16

lol...

Answer 17

pi is approximately 3.14 blah blah
3.14/2 is bigger than one
so .5 is definitely not 1

Answer 18

hmm sorry i'm forgetting my trig..how do you convert from degrees to radians... out of your head ?lol

Answer 19

30 degrees=pi/6 right?
so the question is how do we get from 30 degrees to pi/6
so 30*pi/180
so you just multiply the number in degrees by pi/180 (canceling the degrees on both top and bottom since 180 is in degrees also)

Answer 20

to get from pi/6 to 30 degrees
you multiply pi/6 by 180 degrees/pi

Answer 21

ahh yes ok thank you...it's all coming back now

Answer 22

radians is the same as if we are talk about 1 (it can be integer)
if you want if it makes since you can call your radians normal numbers lol
does that make since
you aren't working with degrees but normal numbers

Answer 23

lol okay

Answer 24

do you have anymore questions

Answer 25

do you have i ti83?

Answer 26

umm just trying to do it using pi/4...but i think i get the hang of it

Answer 27

no...i have a casio fx-350MS is that a graphing calc

Answer 28

go to mode and make sure your calculator is in radians

Answer 29

yes i did that thank you

Answer 30

ok it looks like you are all set cool!

Answer 31

lol thank so much again

Answer 32

:)