Question

9. Find the 10th degree Taylor polynomial for the following functions: a) cos(x2) b) sin(2x) c) ex+1 d) ex? cos(x3)

c,d,e please, clean work, clean handwriting please

Answer 1

© ex+1, The taylor polynomial is given as f +(-) = P(W) = 2 070)_ OX f (x) ~ Pla K=0 KI k- ok! so we need to find the derivatives of given tunction, at a point a. Here we take a=0 so. - t = f(x) = f(0) = e. 017) derivatives + (12 desivatives C) = Alpes CASA D ' - (2+1)' e*t! 1 and f (o)= e. get a polynomial Now use the calculated values to text + 2 + y = P. is the required taylor polynomial for any other polynomical at a=o. If you want post you can change the value as a-

è cosx) = f(i) The results of desvatives for this Bunction are to wide, the reture. I only write Here all the desivatives. Please you you write further polynomial expressin. f(n) = coses) (a) = -x et (se sin(x) – ecos(x)) macm cm -(123° +62) 8014) +(9**_***_2) COS CA')) f2) = 72 { (275 – 36x² 5 + 2²-6) sin(2²) + (-540_462 +123) Cos (7)] + C) = [(216 x' +2782 – 2893? - 120x) sin(x)) + (3128 21646 - 524 x t – 132 x ² +12) cos(x)] FC) = cé [(2432_0.10802_35401 - 960 x++11 403°+12) sin(x) +(-310x900x73308 x + 2720 x++ 240 24) cosce)] - [(-291632" - 297039+ 25344 x+31320* *2250*- 25203) sinu? +(-7 29 x 2 + 4s6ono +19tions + 2764 – 249wn- goou_240) cos x] #G) [(2187x42 20 4123_971464 +15006243147484+ 183/60x7 + 25 20x2 – 25 20) sin(n+ (-102063_7938 x" +16 40sex +25716807 - 2637645 – 125100 x _ 18480x) cos(x)] #W) = (6949927'186084" 931542x"- 1711630x2 253052** +3670288 x 813120 x) sin(x) + (6561216_81698 x 4 439992 x 2 287784x + 29350 48% +231190436 3746 40x7 - 42001272 -18480) cosa ) ( (a) = [(-19683 x ² + 3149282" + 1672072 x t - 25 49 232 x 12 22473720x to 20672496 n + 12292160x + 16087680 x + 24 94 8 wore) sin (180981117 - 17996x's_ 4817232 - 9839232 "+11249707 + 36025056 ** + 15561504* - 23385603 - 876960 7 3385608 - 8T6960x) cos(x)]

Sinca?).fo., {"CO) - - 2x(85963?) + (-?-1) 2013 (32) 2 (x+12 2 (a) = – 2 [(2n + ant - ²+)-sinlan?) + (3 nt+1-1) Cosa3] It az 43 (a) = 4x{(3x² + 3x7 - zu ts) sin(u) + (-23 bu-zu-a) cost?] - 4 [can'”+ 16000 gu²+ 160 +26+7_368²+3) sin(x2) + Conostro – 20+ gruo) costa?) (P-1) in this manner ! (9) 21 082 +4 6080 x of (u) 4 6080 x + 202752x +4354562 +300 384 x + 20 15 8852544x + 8760038 + 14031364 + 43545601 - 21477888 + - 853099 2% + 265305601 - 19656000) since 21 22 +(5124 + 4608 x + Goun - 606722_3568322 - 13 - 1372896n 962 a 3537 + 2840 832xt8951648 x 560437124 +3036211 2x + 5181960n 346852804 + 30887to x I cosx)) write ③. If Catus surther daylor polynomial as written is example Due to heal big steps i skip some steps. you dont like this Answer dont Thumb down. otherwise. Thumb up.