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Questions › JNU › JNU SIS 2018 › Q9
2 marks, −1Mathematics › Limits, continuity and differentiability › Derivatives in economic use: elasticity, growth and inflectionModerateabout 2 min

JNU SIS 2018 Question 9: Limits, continuity and differentiability

Find the rates of growth (rog) of variables XXX and YYY when they are the following continuous functions of time ttt :

I. X=t3X = t^3X=t3

II. Y=Ae∫0tr′(s) dsY = Ae^{\int_0^t r'(s)\,ds}Y=Ae∫0t​r′(s)ds where r′(s)=drdsr'(s) = \dfrac{dr}{ds}r′(s)=dsdr​

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Find the rates of growth (rog) of variables X and Y when they are the following continuous functions of time t: I. X = t³ II. Y = Ae^(∫₀^t r′(s) ds) where r′(s) = dr/ds (A) rog of Y is 3 and rog of X is r(t) (B) rog of Y is 3 and rog of X is ∫₀^t r′(s) ds (C) rog of Y is 3/t and rog of X is r(t) (D) None of the above

Also written as: Find the rates of growth (rog) of variables X and Y when they are the following continuous functions of time t: I. X = t^3 II. Y = Ae^(integral_0^t r'(s) ds) where r'(s) = dr/ds

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Derivatives in economic use: elasticity, growth and inflection, part of Limits, continuity and differentiability in Mathematics.

Interpreting derivatives as growth rates and elasticities, and the meaning of an inflection point.

TestStop has 9 past-paper questions on this subtopic.

Practise Limits, continuity and differentiabilityMore on Derivatives in economic use: elasticity, growth and inflection

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