Chapter 3: Integral Calculus IIJanuary 13, 2025 Maven Leave a Comment Welcome to the Chapter 3: Integral Calculus II Quiz! Name Email 1. If the marginal revenue $MR = 35 + 7x − 3x^{2} , $ then the average revenue AR is $35x+\dfrac{7x^{2}}{2}-x^{3}$ $35+\dfrac{7x}{2}-x^{2}$ $35+\dfrac{7x}{2}+x^{2}$ $35+7x+x^{2}$ None 2. Area bounded by the curve $y = e−2x$ between the limits $0 \le x \le \infty$ is $1 sq.units$ $\dfrac{1}{2} sq.units$ $5 sq.units$ $ 2 sq.units$ None 3. Area bounded by the curve $y =\dfrac{1}{x}$ between the limits 1 and 2 is $log 2 sq.units$ $log 5 sq.units$ $log 3 sq.units$ $log 4 sq.units$ None 4. The given demand and supply function are given by $D(x)= 20 − 5x$ and $S(x) = 4x + 8$ if they are under perfect competition then the equilibrium demand is $40$ $\dfrac{40}{3}$ $\dfrac{41}{2}$ $\dfrac{41}{5}$ None 5. The demand and supply functions are given by $D(x)= 16 − x^{2}$ and $S(x) = 2x^{2} + 4$ are under perfect competition, then the equilibrium price x is $2$ $3$ $4$ $5$ None 6. Area bounded by the curve $y = x (4 − x)$ between the limits 0 and 4 with x − axis is $\dfrac{30}{3} sq.units$ $\dfrac{31}{2} sq.units$ $\dfrac{32}{3} sq.units$ $\dfrac{15}{2} sq.units$ None 7. The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is $9x^{2} + 54x$ $9x^{2} - 54x$ $54x-\dfrac{9x^{2}}{2}$ $54x-\dfrac{9x^{2}}{2}+k$ None 8. The profit of a function p(x) is maximum when $MC − MR = 0$ $MC = 0$ $MR = 0$ $MC + MR = 0$ None 9. If MR and MC denotes the marginal revenue and marginal cost functions, then the profit functions is $P = \displaystyle \int_{}^{}(MR − MC) dx + k$ $P = \displaystyle \int_{}^{}(MR + MC) dx + k$ $P = \displaystyle \int_{}^{}(MR)(MC) dx + k$ $P = \displaystyle \int_{}^{}(R-C)dx + k$ None 10. If the marginal revenue function of a firm is $MR=e^{\frac{-x}{10}}$ then revenue is $-10e^{\frac{-x}{10}}$ $1-e^{\frac{-x}{10}}$ $10 (1-e^{\frac{-x}{10}})$ $e^{\frac{-x}{10}}+10$ None 11. When $x_{0}=5 \; and \; p_{0}=3$ the consumer’s surplus for the demand function $p_{d} = 28 − x^{2} $ is $250 units$ $\dfrac{250}{3}units$ $\dfrac{251}{2}units$ $\dfrac{251}{3}units$ None 12. If MR and MC denote the marginal revenue and marginal cost and $MR − MC = 36x − 3x^{2} − 81, $ then the maximum profit at x is equal to $3$ $6$ $9$ $5$ None 13. The marginal cost function is $MC = 100\sqrt{x}$ find AC given that TC =0 when the out put is zero is $\dfrac{200}{3}x^{\frac{1}{2}}$ $\dfrac{200}{3}x^{\frac{3}{2}}$ $\dfrac{200}{3x^{\frac{3}{2}}}$ $\dfrac{200}{3x^{\frac{1}{2}}}$ None 14. For the demand function p(x), the elasticity of demand with respect to price is unity then revenue is constant cost function is constant profit is constant none of these None 15. The demand function for the marginal function $MR = 100 − 9x^{2}$ is $100-3x^{2}$ $100x-3x^{2}$ $100x-9x^{2}$ $100x+9x^{2}$ None 16. Area bounded by $y = x$ between the lines y = 1, $ y = 2\; with \; y = axis$ is $\dfrac{1}{2}units$ $\dfrac{5}{2}units$ $\dfrac{3}{2}units$ $1 sq.unit$ None 17. When$ x_{0}=2 \; and \; p_{0}=12 $ the producer's surplus for the demand function $p_{S} = 2x^{2}+4$ is $\dfrac{31}{5}units$ $\dfrac{31}{2}units$ $\dfrac{32}{3}units$ $\dfrac{30}{7}units$ None 18. The producer’s surplus when the supply function for a commodity is $P = 3 + x \; and \; x_{0} = 3 $ is $\dfrac{5}{2}$ $\dfrac{9}{2}$ $\dfrac{3}{2}$ $\dfrac{7}{2}$ None 19. The demand and supply function of a commodity are $D(x)= 25 − 2x$ and $S(x) = \dfrac{10+x}{4} $ then the equilibrium price $P_{0}$ is $5$ $2$ $3$ $10$ None 20. The demand and supply function of a commodity are $P(x)= (x − 5)^{2} $ and $ S(x)= x^{2} + x + 3 $ then the equilibrium quantity $x_{0}$ is $5$ $2$ $3$ $1$ None 21. The area bounded by the parabola $y^{2} = 4x$ bounded by its latus rectum is $\dfrac{16}{3}sq.units$ $\dfrac{8}{3}sq.units$ $\dfrac{72}{3}sq.units$ $\dfrac{1}{3}sq.units$ None 22. Area bounded by $ y = x$ between the limits 0 and 2 is $1 sq.units$ $3 sq.units$ $2 sq.units$ $4 sq.units$ None 23. If the marginal revenue of a firm is constant, then the demand function is $MR$ $MC$ $C(x)$ $AC$ None 24. For a demand function p, $if\; \displaystyle \int_{}^{}\frac{dp}{p}=k,\; \displaystyle \int_{}^{}\frac{dx}{x}, \;$ then k is equal to $\eta_{d}$ $-\eta_{d}$ $\dfrac{-1}{\eta_{d}}$ $\dfrac{1}{\eta_{d}}$ None 25. Area bounded by $y = e^{x}$ between the limits 0 to 1 is $( e −1) sq.units$ $( e +1) sq.units$ $( 1-\dfrac{1}{e}) sq.units$ $( 1+\dfrac{1}{e}) sq.units$ None Time's upRelated Posts:Chapter 2: Integral Calculus IChapter 5: Differential CalculusChapter 1: Introduction to Micro EconomicsChapter 2. Consumption Analysis
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