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.
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<h2>Answer with explanation:</h2>
Let x denotes the number of days and y denotes the total change in gas price ( in dollars).
Given : During the past seven days the price of regular gas is decreased by $0.2 each day.
Rate of decrease =$0.2 per day
Then , Total change in gas price = Rate of decrease x Number of days
i.e.
i.e. (1)
To find the total change in gas price in 7 days , we put x= 7 in (1) , we get
Hence, the total change in gas price in 7 days = $1.4