If f x - x - x 2- x 3- x 4- - - x -1- then f - x -A- 1-1-x2B- 1-1-xC- 1-1-x2D- 1-1-x

The correct option is C x x^2+x^3 .....=(x+x^3+x^5+......) (x^2+x^4+x^6+.....) =x/1+x⇒dy/dx=1/(1+x)^2 ...

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Standard XII

Mathematics

Binomial Expression

If f x = x - ...

Question

$I f f (x) = x - x^{2} + x^{3} - x^{4} + . . . . . . . \infty, | x | < 1, t h e n f^{'} (x) =$

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Solution

The correct option is B

$x - x^{2} + x^{3} - . . . . . = (x + x^{3} + x^{5} + . . . . . .) - (x^{2} + x^{4} + x^{6} + . . . . .) = \frac{x}{1 + x} \Rightarrow \frac{d y}{d x} = \frac{1}{(1 + x)^{2}}$

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Q. If

f (x) = x - x^{2} + x^{3} - x^{4} + \dots

and

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If f(x)=x−x2+x3−x4+.......∞,|x|<1, then f′(x)=

The correct option is B x−x2+x3−.....=(x+x3+x5+......)−(x2+x4+x6+.....) =x1+x⇒dydx=1(1+x)2

$I f f (x) = x - x^{2} + x^{3} - x^{4} + . . . . . . . \infty, | x | < 1, t h e n f^{'} (x) =$

The correct option is B

$x - x^{2} + x^{3} - . . . . . = (x + x^{3} + x^{5} + . . . . . .) - (x^{2} + x^{4} + x^{6} + . . . . .) = \frac{x}{1 + x} \Rightarrow \frac{d y}{d x} = \frac{1}{(1 + x)^{2}}$