Let f be a derivable function satisfying the equation -0 x f t dt -0 x t - f x - t dt - e - x -1f -0 has the value equal toA- 2B- 0 C -1-1-D- 1- e

The correct option is A 2 Let f be a derivable function satisfying the equation ∫_0^xf(t)dt+∫_0^xt.f(x t)dt=e^ x 1 Put x = 0 in (2) f’(0) + f(0) = 1 ⇒ f’(0 ...

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Standard XII

Mathematics

Algebra of Derivatives

Let f be a de...

Question

Let f be a derivable function satisfying the equation $\int_{0}^{x} f (t) d t + \int_{0}^{x} t . f (x - t) d t = e^{- x} - 1$

f’(0) has the value equal to

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$1 - \frac{1}{e}$

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$1 + \frac{1}{e}$

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Solution

The correct option is A
2

Let f be a derivable function satisfying the equation $\int_{0}^{x} f (t) d t + \int_{0}^{x} t . f (x - t) d t = e^{- x} - 1$

Put x = 0 in (2)
$f^{'} (0) + f (0) = 1 \Rightarrow f^{'} (0) = 2$

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Let f be a derivable function satisfying the equation ∫x0f(t)dt+∫x0t.f(x−t)dt=e−x−1 f’(0) has the value equal to

The correct option is A 2 Let f be a derivable function satisfying the equation ∫x0f(t)dt+∫x0t.f(x−t)dt=e−x−1 Put x = 0 in (2) f′(0)+f(0)=1⇒f′(0)=2

Let f be a derivable function satisfying the equation $\int_{0}^{x} f (t) d t + \int_{0}^{x} t . f (x - t) d t = e^{- x} - 1$

f’(0) has the value equal to

The correct option is A
2

Let f be a derivable function satisfying the equation $\int_{0}^{x} f (t) d t + \int_{0}^{x} t . f (x - t) d t = e^{- x} - 1$

Put x = 0 in (2)
$f^{'} (0) + f (0) = 1 \Rightarrow f^{'} (0) = 2$