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Calculus · Taylor-Series

Taylor series of cos(x)

\cos{\left(x \right)}

f(x) = \cos{\left(x \right)}
Taylor series about x = 0: f(x) = Σ fᵏ(x₀)/k! · (x − x₀)ᵏ.
f^{(0)}(0) = \cos{\left(x \right)}\big|_{x=0} = 1
Derivative 0 at the centre.
f^{(1)}(0) = - \sin{\left(x \right)}\big|_{x=0} = 0
Derivative 1 at the centre.
f^{(2)}(0) = - \cos{\left(x \right)}\big|_{x=0} = -1
Derivative 2 at the centre.
f^{(3)}(0) = \sin{\left(x \right)}\big|_{x=0} = 0
Derivative 3 at the centre.
f^{(4)}(0) = \cos{\left(x \right)}\big|_{x=0} = 1
Derivative 4 at the centre.
f^{(5)}(0) = - \sin{\left(x \right)}\big|_{x=0} = 0
Derivative 5 at the centre.
\frac{x^{4}}{24} - \frac{x^{2}}{2} + 1
Assemble the terms up to degree 5.

Mutasd meg a választ!

\frac{x^{4}}{24} - \frac{x^{2}}{2} + 1 + O((x-0)^{6})