Let fx be a twice differentiable function and f-0 - 5- then limx - 0 3fx -4f3x - f9xx2 is equal to

Lim_x → 0 3f(x) 4f(3x) + f(9x)x^2 (00 form ) Applying L Hospital's rule lim_x → 0 3f'(x) 12f'(3x) + 9f'(9x)2x (00 form ) = lim_x → 0 3f”(x) 36f”(3x) + 8 ...

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Standard XII

Mathematics

Solving Linear Differential Equations of First Order

Let fx be a t...

Question

Let $f (x)$ be a twice differentiable function and $f^{''} (0) = 5$ , then $lim x \to 0 \frac{3 f (x) - 4 f (3 x) + f (9 x)}{x^{2}}$ is equal to

80

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100

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120

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140

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Solution

The correct option is C $120$
$lim x \to 0 \frac{3 f (x) - 4 f (3 x) + f (9 x)}{x^{2}} (\frac{0}{0} form)$
Applying L- Hospital's rule
$lim x \to 0 \frac{3 f^{'} (x) - 12 f^{'} (3 x) + 9 f^{'} (9 x)}{2 x} (\frac{0}{0} form)$
$= lim x \to 0 \frac{3 f^{''} (x) - 36 f^{''} (3 x) + 81 f^{''} (9 x)}{2}$
$= \frac{3 f^{''} (0) - 36 f^{''} (0) + 81 f^{''} (0)}{2}$
$= 24 f^{''} (0) = 24 (5) = 120$

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Similar questions

Q. Let

f (x)

be a twice differentiable function and

f^{''} (0) = 5

. Then

lim x \to 0 \frac{3 f (x) - 4 f (3 x) + f (9 x)}{x^{2}}

is equal to

Let $f (x)$ be a twice differentiable function and $f^{''} (0) = 5$ , then $l i m x \to 0 \frac{3 f (x) - 4 f (3 x) + f (9 x)}{x^{2}}$ is equal to:

$Let f (x)be a twice differentiable function and f"(0)=5, then l i m x \to 0 \frac{3 f (x) - 4 f (3 x) + f (9 x)}{x^{2}} is equal to:$

Let $f (x)$ be a twice differentiable function and $f^{''} (0) = 5$ , then $l i m x \to 0 \frac{3 f (x) - 4 f (3 x) + f (9 x)}{x^{2}}$ is equal to:

Q. Let

f (x)

be a twice-differentiable function and

f^{''} (0) = 2

then evaluate

lim x \to 0 \frac{2 f (x) - 3 f (2 x) + f (4 x)}{x^{2}}

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Solving Linear Differential Equations of First Order

Standard XII Mathematics

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Let f(x) be a twice differentiable function and f′′(0)=5, then limx→03f(x)−4f(3x)+f(9x)x2 is equal to

The correct option is C 120limx→03f(x)−4f(3x)+f(9x)x2 (00 form) Applying L- Hospital's rule limx→03f′(x)−12f′(3x)+9f′(9x)2x (00 form) =limx→03f′′(x)−36f′′(3x)+81f′′(9x)2 =3f′′(0)−36f′′(0)+81f′′(0)2 =24f′′(0)=24(5)=120

Let $f (x)$ be a twice differentiable function and $f^{''} (0) = 5$ , then $lim x \to 0 \frac{3 f (x) - 4 f (3 x) + f (9 x)}{x^{2}}$ is equal to