Question

aprrox tan(-.1) using Taylor polynomials with n=3

Answer 1

whew only 3 is good

\[\tan(x)=x+\frac{x^3}{3}+\frac{2x^5}{3\times 5}+...\]

Answer 2

put \(x=-.1\) and a calculator, which is really kind of dumb since you can just put \(\tan(-.1)\) directly in to a calculator

Answer 3

Thanks! Can I ask ya another quick question? My next problem says eval sqrt 101 using taylor. Do I just call it sqrt 100 and x=1?

Answer 4

use taylor polynomail witj n=3 to approx. (101)^1/2

Answer 5

yes i think so

Answer 6

use the taylor polynomial for
\[\sqrt{100+x}\]

Answer 7

or x=101 a=0?

Answer 8

use
\[f(x)=\sqrt{100+x}\] because you want to expand around \(x=0\)
then you can put \(x=1\)

Answer 9

how many terms you need?

Answer 10

I think my books answer has a=100? 3 terms

Answer 11

the firt term of answer is 10 hen 1/20 (x-100) .......

Answer 12

ok good
expand about zero get
\[10+\frac{x}{20}\]

Answer 13

should be \(x\) up top, not \(100-x\)

Answer 14

im with ya

Answer 15

you are expanding about 0, the 100 is in the function

Answer 16

i think the next term is \(-\frac{x^2}{800}\) but it is late so i could be wrong

Answer 17

oh yeah wrong! i am off by a zero

Answer 18

thats correct......I managed to get a little lost with it though ); Can I check the derivatives with you?

Answer 19

I can start a new post if youd like for another medal?

Answer 20

sure but it comes with no guarantees

Answer 21

lol no i don't need any more thank you
i got this bike for reaching 1000, after that i can't seem to redeem them anywhere

Answer 22

lol cool

Answer 23

ok so from the biginning ( sorry) werr going to say f(x)= (100+x)^1/2 right

Answer 24

yes

Answer 25

also a=0

Answer 26

yes, aka mclauren

Answer 27

so they say to approx with n=3 so.......ned first 3 derivs.

Answer 28

f'(x)= 1/2(100+x)^1/2

Answer 29

exponent is \(-\frac{1}{2}\) but it is easier to write
\[f'(x)=\frac{1}{2\sqrt{100+x}}\]
you have to evaluate at \(x=0\) so want a the radical form probably

Answer 30

although the form
\[\frac{1}{2}(100+x)^{-\frac{1}{2}}\] is good for taking the second derivative

Answer 31

\[f \prime \prime (x) + -1/4\sqrt{(100+x)^3}\]

Answer 32

yes

Answer 33

and so \(f''(0)=-\frac{1}{4\times 10^3}=-\frac{1}{4000}\)

Answer 34

and \(\frac{f''(0)}{2}=-\frac{1}{8000}\) so you are good to go with three terms

Answer 35

why divide by 2?

Answer 36

ahhhh

Answer 37

2!