If f x -0 x dt -2- t t- thenA- f 21-3D- f 2-1

The correct option is A f(2) lt;1/3f^'(x)=1/2+x^4 By LMVT f^'(C)=f(2) f(1)/2 1 for som c ϵ (1,2) ⇒ f(2)=1/2+c^4 f(1)=0 ⇒ 1 lt;c lt;2⇒ 3 lt; 2 + c^4 ...

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Byju's Answer

Standard XII

Mathematics

Property 5

If f x =∫0 x ...

Question

If $f (x) = \int_{0}^{x} \frac{d t}{2 + t^{4}}$ , then

f (2) < \frac{1}{3}

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f (2) > \frac{1}{3}

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f (2) = \frac{1}{3}

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f (2) > 1

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Solution

The correct option is A $f (2) < \frac{1}{3}$
$f^{^{'}} (x) = \frac{1}{2 + x^{4}}$
By LMVT $f^{^{'}} (C) = \frac{f (2) - f (1)}{2 - 1}$ for som $c ϵ (1, 2)$
$\Rightarrow f (2) = \frac{1}{2 + c^{4}} f (1) = 0 \Rightarrow 1 < c < 2 \Rightarrow 3 < 2 + c^{4} < 18 \Rightarrow f (2) < \frac{1}{3}$

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Similar questions

Q. If

f (x) = \int_{1}^{x} \frac{d t}{2 + t^{4}}

, then

Q. If

f (x), g (x)

are two differentiable functions on

[0, 2]

satisfying

f^{''} (x) = g^{''} (x), f^{'} (1) = 2 g^{'} (1) = 4

and

f (2) = 3 g (2) = 9

, then

f (x - 1) = \frac{x}{3} + f (x)

f (0) = 2

then value of

f (21) = ?

The graph of the function $y = f (x)$ is symmertical about the line $x = 2$ , then

Q. Match the columns:

\begin{matrix} Column I & Column II (a) & X e F_{6} & (p) & Xe(excess) + F_{2} (b) & X e F_{4} & (q) & X e + F_{2} (1 : 4) (c) & X e F_{2} & (r) & X e + F_{2} (1 : 5) (s) & X e + F_{2} (1 : 20) \end{matrix}

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If f(x)=∫x0dt2+t4, then

The correct option is A f(2)<13f′(x)=12+x4 By LMVT f′(C)=f(2)−f(1)2−1 for som cϵ(1,2) ⇒f(2)=12+c4f(1)=0⇒1<c<2⇒3<2+c4<18⇒f(2)<13

If $f (x) = \int_{0}^{x} \frac{d t}{2 + t^{4}}$ , then

The correct option is A $f (2) < \frac{1}{3}$
$f^{^{'}} (x) = \frac{1}{2 + x^{4}}$
By LMVT $f^{^{'}} (C) = \frac{f (2) - f (1)}{2 - 1}$ for som $c ϵ (1, 2)$
$\Rightarrow f (2) = \frac{1}{2 + c^{4}} f (1) = 0 \Rightarrow 1 < c < 2 \Rightarrow 3 < 2 + c^{4} < 18 \Rightarrow f (2) < \frac{1}{3}$