Find the Maclaurin Series for f and find its radius of Convegen 10-х Find the Maclaurin Series for f and find its radius of Convegen 10-х

Question

Question

Answer 1

Answer #1

The Maclaurin series of $f (z)$ is defined as

.3 3! 1!

$\large f'(x)=$ 5/4 4(16-х, X4 16-х)

$f(x)$ d2 5 16-x) 16(16 -x)94

$f(r)$ 45 V16-x64(16 -x)13/4

$f (x)$ 585 16-x) 4x41 dx*V 256 ( 16-X)İ74

$f(0) = 125$

$f(0)-8102$

$45 !(0) = 524288$

$585 f (0) 33554432$

The Maclaurin series is

1 x5x2153 195 x4 -663x5 2 128 16 384 1048576 268435 456 17 179869 184 4641 x6 2 199023 255552 16575 x7 140 737 488 355 328 48

converges when $\large |x|<16$ . Interval of convergence is $\large [-16,16)$

รู้16-r

Radius of convergence is 16

Answer 2

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