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KatRina [158]
3 years ago
9

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

Mathematics
1 answer:
Anon25 [30]3 years ago
6 0

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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Cara and John collect baseball cards.Cara has 12 times as many baseball cards as John.Together they have 117 cards.How many card
enyata [817]

Answer:

Cara:108

Step-by-step explanation:

John: x number of cards

Cara: 12 times x number of cards(she has 12 times more cards than John)

Cara+John=117 cards

12 \times x + x = 117 \\ 13x = 117 \\ x =  \frac{117}{13}  \\ x = 9

Cara has 12×9 cards, so she has 108 cards.

Hope this was helpful :)

5 0
3 years ago
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Find an equation of the tangent line to the graph of the function f(x) = 2sinx at the point where x = pi/3.
BigorU [14]
The equation of the tangent line of f(x) is given by y = f'(x)x + c
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At x = pi/3
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f(pi/3) = 2 sin(pi/3) = √3
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Therefore, required equation is
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Sammy has 4 bags of marbles. Each bag has 12 marbles in it. Which equation represents how many total marbles he has
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Answer:

t = 4 x 12

Step-by-step explanation:

t = total # of marbles

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