1MileCrash said:Homework Statement
Find the first 4 nonzero terms of:
[itex]e^{t}cos(t)[/itex]
Homework Equations
The Attempt at a Solution
I am trying to multiply the terms of two known series for my answer, but I'm not sure how to do it efficiently.
Should I list 4 terms of each series, then multiply them as if they were just normal polynomials?
EDIT, I tried doing that and it is completely unfeasible. What's the correct way?
It wouldn't be that bad. Give it a try.1MileCrash said:Wait, why would you do it that way? Differentiating that 4 function 4 times would be terrible!
Mark44 said:It wouldn't be that bad. Give it a try.
e^tcos(t) is a mathematical expression that represents the exponential function e^t multiplied by the cosine function cos(t).
The first 4 nonzero terms of e^tcos(t) are e^t, te^tcos(t), t^2e^tcos(t), and t^3e^tcos(t).
Finding the first 4 nonzero terms of e^tcos(t) allows us to approximate the value of the function for small values of t, which can be useful in various scientific and mathematical applications.
To calculate the first 4 nonzero terms of e^tcos(t), you can use the Taylor series expansion of the function, which involves taking derivatives of e^tcos(t) and evaluating them at t=0.
The function e^tcos(t) has applications in various fields such as physics, engineering, and economics. For example, it can be used to model the behavior of a damped oscillator in physics or to predict the growth of a population in biology.