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The price elasticity of demand for a commodity is ppx3. Find the demand function if the quantity of demand is 3 when the price is ₹ 2. - Business Mathematics and Statistics

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प्रश्न

The price elasticity of demand for a commodity is `"p"/x^3`. Find the demand function if the quantity of demand is 3 when the price is ₹ 2.

योग
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उत्तर

Price elasticity of demand

`eta_"d" = "p"/x^3`

`(-"p")/x ("d"x)/"dp" = "p"/x^3`

`(-x^3)/x "d"x = "p"/"p" "dp"`

`- x^2  "d"x = "dp"`

Integrating on both sides

`- int x^2  "d"x = int "dp"`

`(-x^3)/3 = "p"+ "k"`  ........(1)

When x = 3 and p = 2

`(-(3)^3)/3 = 2 + "k"`

`(- 27)/3 = 2 + "k"`

⇒ – 9 = 2 + k

∴ k = – 11

Equation (1)

⇒ `(-x^3)/3 = "p" - 11` 

∴ p = `11 - x^3/3`

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Application of Integration in Economics and Commerce
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अध्याय 3: Integral Calculus – 2 - Miscellaneous problems [पृष्ठ ७७]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
अध्याय 3 Integral Calculus – 2
Miscellaneous problems | Q 8 | पृष्ठ ७७

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