let $f (x) = x^{3} - x^{2} - 3 x - 1, g (x) = (x + 1) a$ and $h (x) = \frac{f ( x )}{g ( x )}$ where $h$ is a rational function such that $(1)$ it is continuous everywhere except when $x = - 1, (2) x \to \infty lim h (x) = \infty$ and $(3) x \to - 1 lim h (x) = \frac{1}{2}$ then the value of $h (1)$

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let

f (x) = x^{3} - x^{2} - 3 x - 1, g (x) = (x + 1) a

and

h (x) = \frac{f ( x )}{g ( x )}

where

h

is a rational function such that

(1)

it is continuous everywhere except when

x = - 1, (2) x \to \infty lim h (x) = \infty

and

(3) x \to - 1 lim h (x) = \frac{1}{2}

then the value of

h (1)

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Question Text

let

f (x) = x^{3} - x^{2} - 3 x - 1, g (x) = (x + 1) a

and

h (x) = \frac{f ( x )}{g ( x )}

where

h

is a rational function such that

(1)

it is continuous everywhere except when

x = - 1, (2) x \to \infty lim h (x) = \infty

and

(3) x \to - 1 lim h (x) = \frac{1}{2}

then the value of

h (1)

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