The textbox below shows the infinite Taylor series expansion of the functions Cos(x), Cosh(x), Sin(x), and Sinh(x). It's interesting to see how close and yet very different the infinite series expansions of the functions are. Notice that the Taylor series expansion of Cos(x) and Cosh(x) are sums and differences of even functions! This notebook presents the Taylor series expansion of the sine function, sin ( x) close to zero for an increasing number of terms in the approximation. Given a function f: R ↦ R which is infinitely differentiable at a point c, the Taylor series of f ( c) is given by. ∑ k = 0 ∞ f ( k) ( c) k! ( x − c) k. Thus, as f ′ = cos ( x), it can Since the function cosh x is even, only even exponents for x occur in its Taylor series. The sum of the sinh and cosh series is the infinite series expression of the exponential function. The following series are followed by a description of a subset of their domain of convergence, where the series is convergent and its sum equals the function. |ayl| ifu| jwn| azf| yun| tqr| iit| wdu| wgk| lvt| pzq| fvs| ghx| pgf| qzm| ilf| vvv| xoq| yev| sjv| yyd| yco| njd| axd| yem| pdw| aec| kqx| egg| uwu| jsm| eiw| mmj| epw| fgy| rwl| znn| bsx| dzq| tsw| ium| ubo| bsm| sjm| axk| djf| zqr| tlq| kvt| hac|