cosh(x+y) = [e^(x+y) + e^(-x-y)]/2 = [e^x * e^y + e^-x * e^-y]/2 = [e^x * e^y + e^x * e^-y +e^-x * e^y + e^-x * e^-y]/4 + [e^x * e^y - e^x * e^-y -e^-x * e^y + e^-x * e^-y]/4 = (e^x + e^-x)(e^y + e^-...
最大头的地方出现在有关inverse的integration,也就是结果出现arc和ar家族的题目,这里所有的结果都可以在formula booklet查到,总之,分母中遇到x^2和a^2式子,翻formula就对了!要注意的是两点:1. 如果碰到2x^2,那就需要把2提出来,尤其是有根号的情况,提出来的是root 2;2. 如果有x^2+2x-4这种带有linear term...
if f(x)is continuous and differentiable. 1)导数(瞬时变化率) f(x)f'(x)f''(x) s v a 2)critical points驻点 f'(x)=0 stationary points 3)inflection points拐点 f''(x)=0 f'(x)≠0 4)local(relative)max&min最大值最小值 max f'(x)=0 f''(x)<0 min f'(x)=0 f''(x)>0 5...
值域(range)是y的取值范围,一般会根据x的取值范围有所变化。 在求一个function的range时,一定要想清楚x等于多少时会导致y最小/最大。比如,三角函数和二次函数中,往往当x的值是特殊值而不是最小/最大值时,y才会取到极端的值。 1复合函数 学习了函数的基本定义后,我们将要计算多个函数组合后的情况: 当将两...
J Meixner The meaning of Christoffel's sum formula for expansions in orthogonal polynomials P.L Butzer, F Feher (Eds.), E. B. Christoffel, Birkhäuser-Verlag, Basel (1981), pp. 160-171 [In German] CrossrefGoogle Scholar [Mh1] H.N Mhaskar Weighted analogues of Nikolskii-type inequaliti...
if f(x)is continuous and differentiable. 1)导数(瞬时变化率) f(x)f'(x)f''(x) s v a 2)critical points驻点 f'(x)=0 stationary points 3)inflection points拐点 f''(x)=0 f'(x)≠0 4)local(relative)max&min最大值最小值 max f'(x)=0 f''(x)<0 ...
Integral Formula: For solving this problem, we have to understand evaluation of an integration using the power rule: Basically power rule is method to evaluate the integration of an algebraic functionxnwherenis a real number. The power formula of the integration is given by:∫xndx=xn+1n+1+C...
(specifically miR-200a-5p and miR-141-3p) presents as potential targets several mRNAS involved in sperm quality, fertilization success and male sex differentiation such as:dmrt1andkitamRNAs (Fig.4C).dmrt1andkitatranscripts were analysed by qPCR comparing to good and bad zebrafish breeders in ...
Because we are considering the graph of y = x2, we know that y + dy = (x + dx)2. Image As we let dx become zero we are left with just 2x, and this is the formula for the gradient of the tangent at P. We have a concise way of expressing the fact that we are letting dx...
结合律:\mathcal{(X\circ Y)\circ Z=X\circ(Y\circ Z)} 在一个李群中,流形在每一点上看起来都是一样的(比如在一个球面上,参见例1和例2),因此所有在任何点上的切线空间都是相同的。群结构强加于流形上元素的组合仍然保持在流形上。(1),并且每个元素在流形中也存在一个逆,这些元素中的一个特殊是...