Calculus Help!!
Find the fifth degree Taylor polynomial approximation T _{5}(x) centered at a=0 to the function f(x)=cos(x);f(x)=sin(x);f(x)=e^{x}

Question

Calculus Help!!
Find the fifth degree Taylor polynomial approximation T _{5}(x)  centered at a=0  to the function f(x)=cos(x);f(x)=sin(x);f(x)=e^{x}

anonymous · Answer

$$T _{5}(x)$$

anonymous · Answer

f(x)=cos(x)
f(x)=sin(x)
$$f(x)=e ^{x}$$

anonymous · Answer

i tried put 1,0,1 and it is not correct!!

anonymous · Answer

i tried to put x^8/8!,x^9/9!,x^4/4! and it is not correct either!!

anonymous · Answer

anonymous · Answer

for cos(x),i put 1-x^2/2!+x^4/4!-x^6/6! and it is wrong

anonymous · Answer

should i put one more term?

anonymous · Answer

there sould be 6 term..

anonymous · Answer

when should i put 6 terms and when should i put 5 terms and when should i put 4 terms?

anonymous · Answer

is it because it is an even power function?

anonymous · Answer

degree means how many derivation you need to have, so in your case 5 dervative plus f(x)

anonymous · Answer

Thanks a lot!!

anonymous · Answer

but how come for sin(x) ,it is x-x^3/3!+x^5/5!-x^7/7!

anonymous · Answer

attachment

anonymous · Answer

Thank you!!

anonymous · Answer

attachment

anonymous · Answer

yw

anonymous · Answer

i am sorry.can you reattach it.it is kind of small that i can't really see==

anonymous · Answer

attachment

anonymous · Answer

way better now!!thanks!!

anonymous · Answer

now you can solve for cosx right

anonymous · Answer

yea.I got it!!Thanks a lot!!

anonymous · Answer

you can check your solution here, look at trigonometric func.. http://en.wikipedia.org/wiki/Taylor_series

anonymous · Answer

Thank you so much!! you are awesome=))

anonymous · Answer

np (: