Question

Find the first 4 terms of the taylor series for the function about the point a.

1/sqrt(1+x)

Answer 1

http://en.wikipedia.org/wiki/Taylor_series#Definition

Answer 2

this means we need first 3 derivatives of the function....they dont give a value for "a" ?

Answer 3

First 4 derivatives.

Answer 4

@Lessis , no 1st term is just original function

Answer 5

im sorry its not a its 0....ive been doing this stupid math for way too long:/

Answer 6

Usually, the first term of the taylor series isn't counted, since it's just f(a) (And the taylor polinomial of grade n is f(a) plus the first n derivatives).

Derivating that is going to be a chore though.

Answer 7

@megannicole51 haha ok thought so

Answer 8

its seriously been a long day/night my bad!

Answer 9

lol! nice catch @dumbcow

Answer 10

ok what is 1st derivative?

Answer 11

-1/2(x+1)^(3/2)

Answer 12

second derivative is ((3)/(4(x+1)^(5/2)))

Answer 13

yes...exponents are neg right

Answer 14

no

Answer 15

should be , you started with power of (-1/2) then each time you take derivative you subtract 1

Answer 16

oh ok

Answer 17

It really depends on how you're writing it. If your power is already in the denominator, there is no need to add a minus sign to it.

Answer 18

okay

Answer 19

now what?

Answer 20

sub in 0 for x
then use formula for taylor series

you still need 3rd derivative i think

Answer 21

f'(0)=-1/2
f''(0)=3/4
f'''(0)=-15/8
f''''(0)=105/16

Answer 22

yep

Answer 23

Taylor series
\[1-\frac{1}{2}x+\frac{3}{8}x^{2}-\frac{5}{16}x^{3}\]

Answer 24

yay:) thank you!

Answer 25

yw