# Question:Taylor Series with Maple ...hm.

## Question:Taylor Series with Maple ...hm.

Maple

hi,

i've a mathe exercise with the taylor series that i did on paper. i use maple to solve my tasks but now i have a situation where i am sure that i am not wrong but maple tells me something other

my function

f(x) = sqrt(x-1)

x_o = 5

i derivated the function tree times

f'(x) = (1/2)(x-1)^(-1/2)

f''(x) = -(1/4)(x-1)^(-3/2)

f'''(x) = (3/8)(x-1)^(-5/2)

for my x_o
f(5) = 2

f'(5) = 0.25

f''(5)=-0.03125

f'''(5) = 0.011171875

so my series looks like this for x_o

T(x) = 2 + (0.25/1!)*(x-5)^1 + (-0.03125/2!)*(x-5)^2 + (0.0117185/3!)*(x-5)^3

the same job done with maple :

f:=x->sqrt(x-1);
convert(taylor(f(x),x=5,4),polynom):
T:=unapply(%,x);

T = 3/4 + 1/4x - 1/64(x-5)^2 + 1/512(x-5)^3

why does maple gives me as a result of the first "block" 3/4 i'm quite sure that f(5) = sqrt(5-1) = 2

its just the first value that differs from my paperwork but i don't get what maple does to get the result -> 3/4

thx for help

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