Let f be a real valued function satisfying f x - y - f x - f y and Lt x - 0 f 1- x - x -3- The area bounded by the curve y - f x - the y-axis and the liney -3 isA- 9 eB- None C- 2 eD- 3e

The correct option is D 3ef^1(x)=h→0Ltf(x+h) f(x)/h=h→0Ltf ( 1+h/x )/h/x.x=3/x ...

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Standard XII

Mathematics

Point of Inflection

Let f be a re...

Question

Let f be a real valued function satisfying $f (\frac{x}{y}) = f (x) - f (y)$ and $L t x \to 0 \frac{f (1 + x)}{x} = 3$ . The area bounded by the curve y=f(x), the y-axis and the line y=3 is

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Solution

The correct option is C 3e
$f^{1} (x) = L t h \to 0 \frac{f (x + h) - f (x)}{h} = L t h \to 0 \frac{f (1 + \frac{h}{x})}{\frac{h}{x} . x} = \frac{3}{x}$

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Let f be a real valued function satisfying f(xy)=f(x)−f(y) and Ltx→0f(1+x)x=3. The area bounded by the curve y=f(x), the y-axis and the line y=3 is

The correct option is C 3ef1(x)=Lth→0f(x+h)−f(x)h=Lth→0f(1+hx)hx.x=3x

Let f be a real valued function satisfying $f (\frac{x}{y}) = f (x) - f (y)$ and $L t x \to 0 \frac{f (1 + x)}{x} = 3$ . The area bounded by the curve y=f(x), the y-axis and the line y=3 is

The correct option is C 3e
$f^{1} (x) = L t h \to 0 \frac{f (x + h) - f (x)}{h} = L t h \to 0 \frac{f (1 + \frac{h}{x})}{\frac{h}{x} . x} = \frac{3}{x}$