Question-46907

Question Number 46907 by Raj Singh last updated on 02/Nov/18

Answered by ajfour last updated on 02/Nov/18

y = (x^{2} + 3) (x^{3} - 5)

y + △ y = [{(x + △ x)}^{2} + 3] [{(x + △ x)}^{3} - 5]

△ y = {(x + △ x)}^{5} + 3 {(x + △ x)}^{3}

- 5 {(x + △ x)}^{2} - 15

- x^{5} - 3 x^{3} + 5 x^{2} + 15

= {(x + △ x)}^{5} - x^{5} + 3 [{(x + △ x)}^{3} - x^{3}]

- 5 [(x + △ x) - x]

= (△ x) [5 x^{4} + 3 \times 3 x^{2} - 5 \times 2 x + △ x (\dots)]

\Rightarrow \lim_{△ x \to 0} \frac{△ y}{△ x} = 5 x^{4} + 9 x^{2} - 10 x

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t o c h e c k :

\frac{d y}{d x} = 2 x (x^{3} - 5) + 3 x^{2} (x^{2} + 3)

= 5 x^{4} + 9 x^{2} - 10 x .

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