Let g (x) = \sqrt{\frac{2018}{f \left(\right. x \left.\right)}} be a function such that domain of g (x) is (– 5, 2) \cup (2, 4) where f (x) is a polynomial of least degree equal to 'n' and y-intercept of f (x) is 80. Then

Engineering

Mathematics

Properties of Definite Integral

Question

Let g (x) = $\sqrt{\frac{2018}{f (x)}}$ be a function such that domain of g (x) is (– 5, 2) $\cup$ (2, 4) where f (x) is a polynomial of least degree equal to 'n' and y-intercept of f (x) is 80. Then

the value of 'n' is equal to 3.

$\underset{x \to 2}{Lim} \frac{f (x)}{x^{2} - 3 x + 2} = 0$

$\int_{3}^{5} \frac{(x^{2} + x - 20)}{f (x)} dx = \frac{2}{3}$

the value of f ' (4) equals – 36.

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f (x) = – (x – 4)(x + 5)(x – 2)²