求方程\(x = \cos x\)根的牛顿迭代公式是 。
A: \({x_{n + 1}} = {x_n} - { { {x_n} - \cos {x_n}} \over {1 + \sin {x_n}}},n = 0,1,2 \cdots \)
B: \({x_{n + 1}} = {x_n} + { { {x_n} - \cos {x_n}} \over {1 + \sin {x_n}}},n = 0,1,2 \cdots \)
C: \({x_{n + 1}} = {x_n} - { { {x_n} - \sin {x_n}} \over {1 + \sin {x_n}}},n = 0,1,2 \cdots \)
D: \({x_{n + 1}} = {x_n} - { { {x_n} - \cos {x_n}} \over {1 + \cos{x_n}}},n = 0,1,2 \cdots \)
A: \({x_{n + 1}} = {x_n} - { { {x_n} - \cos {x_n}} \over {1 + \sin {x_n}}},n = 0,1,2 \cdots \)
B: \({x_{n + 1}} = {x_n} + { { {x_n} - \cos {x_n}} \over {1 + \sin {x_n}}},n = 0,1,2 \cdots \)
C: \({x_{n + 1}} = {x_n} - { { {x_n} - \sin {x_n}} \over {1 + \sin {x_n}}},n = 0,1,2 \cdots \)
D: \({x_{n + 1}} = {x_n} - { { {x_n} - \cos {x_n}} \over {1 + \cos{x_n}}},n = 0,1,2 \cdots \)
举一反三
- (1). 设随机变量 \( X_n \),服从二项分布 \( B(n,p) \) 其中 \( 0< p< 1,n=1,2,\cdots \),那么,对于任意实数 \( x \),有 \( \mathop {\lim }\limits_{n\to +\infty } P\left\{{\frac{X_n -np}{\sqrt {np\left( {1-p} \right)} }< x} \right\}= \)()。
- \( {1 \over {1 + x}} \)的麦克劳林公式为( )。 A: \( {1 \over {1 + x}} = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \) B: \( {1 \over {1 + x}} = 1 + x + {x^2} + \cdots + {x^n} + o\left( { { x^n}} \right) \) C: \( {1 \over {1 + x}} = 1 - x + {x^2} - \cdots + {( - 1)^n}{x^n} + o\left( { { x^n}} \right) \) D: \( {1 \over {1 + x}} = 1 - x - { { {x^2}} \over 2}- \cdots - { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \)
- \( {1 \over {1 + x}} \)的麦克劳林公式为( ). A: \( {1 \over {1 + x}} = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \) B: \( {1 \over {1 + x}} = 1 + x + {x^2} + \cdots + {x^n} + o\left( { { x^n}} \right) \) C: \( {1 \over {1 + x}} = 1 - x + {x^2} - \cdots + {( - 1)^n}{x^n} + o\left( { { x^n}} \right) \)
- 下列定义的映射中, ___ 不是内积. A: \(\langle x,y \rangle \triangleq xy ,x,y \in \mathbb{R}\) B: \(\langle (x_1,\cdots,x_n),(y_1,\cdots,y_n) \rangle \triangleq \Sigma_{i=1}^{n}x_iy_i,(x_1,\cdots,x_n),(y_1,\cdots,y_n)\in \mathbb{R}^n\) C: \(\langle f,g \rangle \triangleq \int_a^b f(x)g(x)\mathrm{d}x ,f,g \in C([a,b])\)(\([a,b]\)上连续实函数全体) D: \(\langle (x_1,\cdots,x_n),(y_1,\cdots,y_n) \rangle \triangleq \Sigma_{i,j=1}^{n}a_{ij}x_iy_i,(x_1,\cdots,x_n),(y_1,\cdots,y_n)\in \mathbb{R}^n,A = (a_{ij})是实对称方阵\)
- \( \sin x \)的麦克劳林公式为( ). A: \( \sin x = x - { { {x^3}} \over {3!}} + { { {x^5}} \over {5!}} - \cdots + {( - 1)^n} { { {x^{2n + 1}}} \over {\left( {2n + 1} \right)!}} + o\left( { { x^{2n + 2}}} \right) \) B: \( \sin x = 1 - { { {x^2}} \over {2!}} + { { {x^4}} \over {4!}} - { { {x^6}} \over {6!}} + \cdots + {( - 1)^n} { { {x^{2n}}} \over {\left( {2n} \right)!}} + o\left( { { x^{2n + 1}}} \right) \) C: \( \sin x = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \)