Chapter 3: Integral Calculus IIJanuary 13, 2025 Maven Leave a Comment Welcome to the Chapter 3: Integral Calculus II Quiz! Name Email 1. 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 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. The profit of a function p(x) is maximum when $MC − MR = 0$ $MC = 0$ $MR = 0$ $MC + MR = 0$ None 4. 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 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. 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 7. 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 8. 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 9. 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 10. 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 11. 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 12. 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 13. 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 14. 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 15. 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 16. 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 17. 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 18. 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 19. 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 20. 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 21. 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 22. 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 23. 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 24. 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 25. If the marginal revenue of a firm is constant, then the demand function is $MR$ $MC$ $C(x)$ $AC$ 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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