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A function f satisfy the condition f(...

A function f satisfy the condition ` f(x) = f' (x) + f'' (x) + f'''(x)+. . . . ` where f(x) is a differentiable function indefinitely and dash denotes the order of derivative. If f(0) = 1, then f(x) is a)`e^(x//2)` b)`e^(x)` c)`e^(2x)` d)`e^(4x)`

A

`e^(x//2)`

B

`e^(x)`

C

`e^(2x)`

D

`e^(4x)`

Text Solution

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The correct Answer is:
A
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