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1. ### Taylor Expansion and Error

Homework Statement For g=Hf = sin (f), use a Taylor expansion to determine the range of input for which the operator is approximately linear within 10 % Homework Equations The taylor series from 0 to 1 , the linearization, is the most appropriate equation The Attempt at a Solution...
2. ### Linearizing a system using a taylor expansion

I agree with what you're saying. That's why I didn't think the problem was as hard as it I was thinking. No function is explicitly defined.
3. ### Linearizing a system using a taylor expansion

Homework Statement Linearize the system operator illustrated below by applying a Taylor series expansion. f(t) ----> e^f(t) -----> g(t) Homework Equations I only find the general form of a taylor series relevant. g(x)= sum (0,infinity) of [f^n*(a)*(x-a)^n]/n! The system is...
4. ### Independent Condition Probability Problem

Hello, I had this problem to do for statistics. I am pretty sure I did the first two parts correct. The third, I am not so sure about. I'd appreciate and guidance. A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume...
5. ### Fourier Series Help

My new basis of thought is that the a(n) Fourier coefficient can only be positive 6/npi... is this correct... if figure when you add the negative term, the coefficient becomes zero again. At no point can it be negative. Correct me if I am wrong. Thanks
6. ### Fourier Series Help

Can anyone help me out with this? Find the steady state periodic solution of the following differential equation. x''+10x= F(t), where F(t) is the even function of period 4 such that F(t)=3 if 0<t<1 , F(t)=-3 if 1<t<2. Im basically just having a problem findind the general Fourier...
7. ### Help Solving a differential equation

Hello, i was wondering if someone can help me along with solving this differential equation. (x+2y)y'=y I believe you use substitution. Right now I am setting my substitution to v=(x+2y), but then when i follow through with my work, it doesn't simplify down to a seperable or first order...