how do i determine the value of the coefficients of this?
2Ae^x + B + Cx = 5e^x -162x
Stacey Warren - Expert brainly.com
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Remember Coefficients are the numbers in front of your variables. Variables are x , y, m , d... etc... letters. So the value of the coefficients will be the number in front of your variables... right?
You match the coefficients with the corresponding terms. The e^x terms on both sides of the equation have to be the same, so A=5/2. Similarly, C=-162 and B=0.
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Do you understand my explanation?
how did they match?
On the LHS, there are three terms, the e^x term, the x term, and a constant term. On the right hand side, there are two, just the e^x term and the x term. If the LHS=RHS, the corresponding terms have to be equal. That means 2A=5, and C=-162. Since there is no constant term on the RHS, B=0.
why is it that the answer on my book is C=-18 and A=1/2
I have no idea. I know that my answer solves the question you stated at the top.
i'll just figure it out. thanks a lot. :) can you answer another question? please.
This has to do with the linear independence of the functions. You can't state a linear function in terms of a constant or an exponential, or visa-versa. So the exponential part has to match the exponential part on the other side, the linear part has to match the linear part on the other side, and the constant part has to match the constant part on the other side.