Question

What is the eigen value of the function e^ax when operated on the operator d^n/dx^n?
(A) a^n
(B) xa^n
(C) a^ne^x
(D) a^n/e^x
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Answer 1

Answer:

थे आंसर इस ऑप्शन c

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Answer 2

The correct answer is option (C) a^ne^x.

Explanation:

• a^ne^x is the eigen value of the function e^ax when operated on the operator d^n/dx^n.
• The function exp (ax) is called an eigenfunction of the operator d/dx with an eigenvalue a.
• The function sin (ax) is not an eigenfunction of d/dx because on operating on the function by the operator d/dx, we do not get a constant multiplied by the same function.
• For a given linear operator T : V → V , a nonzero vector x and a constant scalar λ are called an eigenvector and its eigenvalue, respec- tively, when T(x) = λx. For a given eigenvalue λ, the set of all x such that T(x) = λx is called the λ-eigenspace.