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The Amount of Pollution Content Added in Air in a City Due to X Diesel Vehicles is Given by P(X) = 0.005x3 + 0.02x2 + 30x. - Mathematics

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प्रश्न

The amount of pollution content added in air in a city due to x diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above questions ?

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उत्तर

Since, marginal increase in the pollution content is the rate of change of total pollution with respect to the number of diesel vehicles, we have

Marginal increase in pollution = 

\[\frac{d P}{d x} = 0 . 015 x^2 + 0 . 04x + 30\] 
When x = 3, marginal increase in pollution = \[0 . 015\left( 9 \right) + 0 . 04\left( 3 \right) + 30 = 0 . 135 + 0 . 12 + 30 = 30 . 255\]
Hence, the required marginal increase in pollution is 30.255 units.
It indicates the pollution level due to x diesel vehicles.
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पाठ 13: Derivative as a Rate Measurer - Exercise 13.3 [पृष्ठ २४]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 13 Derivative as a Rate Measurer
Exercise 13.3 | Q 9 | पृष्ठ २४

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