(e)Prove exp is a periodic function with period2πi. Induct Euler's formula first. Lemma:∀t∈R,|eit|=1. For∀z=a+bi(a,b∈R),|z|2=(a+bi)(a−bi)=zz¯. exp(it)=∑k=0∞(it)2k2k!+∑k=0∞(it)2k+1(2k+1)!exp(−it)=∑k=0∞(it)2k2k!−∑k=0∞(it)2k...
用二次公式解二次方程 36-Solving Quadratics by Using the Quadratic Formula 06:55 用综合除法和有理根求解高次多项式 37-Solving Higher-Degree Polynomials by Synthetic Division 09:22 操作有理表达式简化和操作 38-Manipulating Rational Expressions Simplification and Operations 09:30 在代数有序对和坐标...
Using subjects familiar with the exponential function discounting formula, this study finds that individuals undervalue the compound interest discounting formula given by the exponential function and overvalue the simple interest discounting formula given by the linear function. These findings can be ...
Another important formula for the exponential function is theBaker-Campbell-Hausdorff formula. Theorem 2 (Baker-Campbell-Hausdorff formula)etA⋅etB=exp(t(A+B)+t22[A,B]+t312([A,[A,B]]−[B,[A,B]])+O(t4))where[A,B]=AB−BA. ...
The exponential function ex is an integral transcendental function. It can be expanded in the power serieswhich converges throughout the z-plane. Equation (1) can also serve as a definition of the exponential function. Letting z = x + iy, L. Euler obtained (1748) the formula ...
In contrast, if a base-10 exponential function has an exponent oflog xandxequals 1000, the result will be 1000. 10(logx)= 10(log 1000)= 103= 1000 Exponential functions can take many other forms and include additional constants. But they all follow the same basic formula and use a varia...
1.Sketch a graph of the exponential function g(x)=5^x.Then use the derivative formulaf'(x) = lim f'(x)=lim [f(x+h)-f(x)]/h to estimate f'(5),f'(0),and f'(10)(this can be done using the table on youh→0graphing calculator,but make sure you write down the formula ...
一道数学数学题目(英文的)是关于导函数的!1.Sketch a graph of the exponential function g(x)=5^x.Then use the derivative formulaf'(x) = lim f'(x)=lim [f(x+h)-f(x)]/h to estimate f'(5),f'(0),and f'(10)(this can be done using the table
Learn more about this topic: Exponential Growth & Decay | Formula, Function & Graphs from Chapter 10 / Lesson 2 219K What is an exponential growth function? Learn the exponential growth and exponential decay formulas and find out wha...
指数的;exponential function 指数函数;exponential growth/decay 指数增长/衰减;exponential model 指数模型 power n. 方,幂(结果) x^n: nth power of x ; if n is negative or non-integer, we say x to the (power of) n , instead. Middle English: from Anglo-Norman French poeir, from an ...