Suppose f(x) is a function such that for some positive integer n, f has n linearly dependent derivatives. In other words, if f(x
),f′(x),…,f(n−1)(x),f(n)(x) are all linearly dependent functions, then f(x) is expressible in terms of a,xk,eax,sin(ax),cos(ax), and any combination of such functions, where a is a constant and k is a positive integer. Prove this statement
1 answer:
Answer:
See explaination for the prove of the statement.
Step-by-step explanation:
To establish this prove, lets refer back to what we already know.
We know that "If the set of reactions {d1,d2,d3,......dn} in a vector space V over a field f be linearly dependent, then atleast one of the vectors of the set can be expressed as a linear combination of the remaining others.
Please kindly go to attachment for a detailed step by step explaination of the prove.
You might be interested in
<h2>Answer:</h2>
Luke does a work of 308Nm
<h2>Step-by-step explanation:</h2>
If we have a constant force that acts on a body in the same direction as the displacement
, then the work
is defined as the product of the force magnitude
and the displacement magnitude
. In other words:
, which is valid for a constant force in direction of straight-line displacement.
In this problem:
Therefore: