Home
Class 12
MATHS
A function f satisfies the condition f(x...

A function f satisfies the condition `f(x)=f'(x)+f''(x)+f'''(x)+…,` where f(x) is a differentiable function indefinitely and dash denotes the order the derivative. If f(0) = 1, then f(x) is

A

`e^(x//2)`

B

`e^(x)`

C

`e^(2x)`

D

`e^(4x)`

Text Solution

AI Generated Solution

To solve the problem, we start with the given condition for the function \( f(x) \): \[ f(x) = f'(x) + f''(x) + f'''(x) + \ldots \] ### Step 1: Set up the equation We can express this condition as: ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Linked Comprehension Type|24 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

A function f satisfies the condition f(x)=f^(prime)(x)+f''(x)+f'''(x)....+infinity ,w h e r ef(x) is a differentiable function indefinitely and dash denotes the order of derivative. If f(0)=1,t h e nf(x) is e^(x/2) (b) e^x (c) e^(2x) (d) e^(4x)

The function f(x) satisfying the equation f^2 (x) + 4 f'(x) f(x) + (f'(x))^2 = 0

Let F(x)=1+f(x)+(f(x))^2+(f(x))^3 where f(x) is an increasing differentiable function and F(x)=0 hasa positive root, then

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuously differentiable function with f'(x)ne0 and satisfies f(0) = 1 and f'(0) = 2 then lim_(xrarr0) (f(x)-1)/(x) is

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=

A function f : R→R satisfies the equation f(x)f(y) - f(xy) = x + y ∀ x, y ∈ R and f (1)>0 , then

A differentiable function f(x) satisfies f(0)=0 and f(1)=sin1 , then (where f' represents derivative of f)

A polynomial function f(x) satisfies the condition f(x)f((1)/(x))=f(x)+f((1)/(x)) . If f(10)=1001, then f(20)=

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

Home
Profile