Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that
Rn(x) → 0.]
f(x) = 4 sinh 4x
f(x)= sum n=0 to infinity ________?

Question

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that 
Rn(x) → 0.]
f(x) = 4 sinh 4x
f(x)= sum n=0 to infinity ________?

anonymous · Answer

i found (x^(2n+1)/((2n+1)factorial)) ????????

perl · Answer

can you define sinh x

anonymous · Answer

0,1,0,1,0 ???

perl · Answer

no i mean, in terms of e^x

perl · Answer

whats the derivative of sinh x , cosh x ?

perl · Answer

ok sinh and cosh have nice property

perl · Answer

sinh x '  = cosh x 
cosh x ' = sinh x

anonymous · Answer

so is my answer correct:S

perl · Answer

OS crashed :(

perl · Answer

f(x) = f(0) + f ' (0) x + f '' (0)/2! * x^2 + f ' ' ' (0) / 3! + ...

f(x) = 4sinh(4x)
f'(x) = 4 cosh (4x)*4 = 16 cosh (4x)

f '' (x) = 16 sinh(4x) * 4 = 64 sinh(4x) 
f'''(x) = 256 cosh(x)
f''''(x) = 1024 sinh (x)


f(0) = 0
f'(0)= 16
f ''(0) = 0
f '''(0) = 256

perl · Answer

a much simpler solution is , we know the Maclaurin series for sinh x : |dw:1386708216057:dw|