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قدم ب قدم

1. f(x) = \cos{\left(x \right)}

   Taylor series about x = 0: f(x) = Σ fᵏ(x₀)/k! · (x − x₀)ᵏ.

2. f^{(0)}(0) = \cos{\left(x \right)}\big|_{x=0} = 1

   Derivative 0 at the centre.

3. f^{(1)}(0) = - \sin{\left(x \right)}\big|_{x=0} = 0

   Derivative 1 at the centre.

4. f^{(2)}(0) = - \cos{\left(x \right)}\big|_{x=0} = -1

   Derivative 2 at the centre.

5. f^{(3)}(0) = \sin{\left(x \right)}\big|_{x=0} = 0

   Derivative 3 at the centre.

6. 1 - \frac{x^{2}}{2}

   Assemble the terms up to degree 3.

جواب کھوليں

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