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Serggg [28]
3 years ago
14

Use a known maclaurin series to obtain the maclaurin series for the given function. f(x = 8x2 tan?1(7x3

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
6 0
Going out on a limb here and guessing that the function is

f(x)=8x^2\tan^{-1}(7x^3)

Please correct me if this isn't the case.

Recall that

\tan^{-1}x=\displaystyle\sum_{n\ge0}\frac{(-1)^nx^{2n+1}}{2n+1}

which converges for |x|.

It follows that

8x^2\tan^{-1}(7x^3)=8x^2\displaystyle\sum_{n\ge0}\frac{(-1)^n(7x^3)^{2n+1}}{2n+1}
=\displaystyle\sum_{n\ge0}\frac{56(-49)^nx^{6n+3}}{2n+1}
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9x+2y-27z=-155 -11x-y+37z=208 19x+6y-52z=-304
Paladinen [302]

Answer:

(x,y,z)=( -2, -1 ,5)

Step-by-step explanation:

9x+2y-27z=-155                                                        (1)

-11x-y+37z=208                                                        (2)

19x+6y-52z=-304                                                     (3)

(1) *3   ;(2) *6     ;(3)*1, you have

27x+6y-81z=-465                                                      (1)

-66x-6y+222z=1248                                                 (2)

19z+6y-52z=-304                                                      (3)


(1) +(2), you have

-39x+141z= 783                                                       (4)

(4) /3, you have

-13x +47z=261                                                          (4)


(2) +(3), you have

-47x+170z=944                                                       (5)


From ( 4) and (5), you have equations

-13x +47z=261                                                         (4)

 -47x+170z=944                                                       (5)


(4)*(-47);    (5)*13,  you have

611x-2209z=-12,267                                              (4)

-611x+2210z=12,272                                              (5)


(4)+(5), you have

z=5

Replace z=5 in (4), you have

611x- 2209*5=-12,267

611x- 11,045 =-12,267

611x=-1222

x= -2

Replace x=-2, z=5 in (1) , you have

9*(-2) +2y -27*5=-155

-18+2y-135=-155

-18+2y=-20

2y=-2

y=-1

Result (x,y,z)=( -2, -1 ,5)









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