Concept explainers
Steady states If a function f represents a system that varies in time, the existence of
74. The population of a colony of squirrels is given by
Trending nowThis is a popular solution!
Chapter 2 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Glencoe Math Accelerated, Student Edition
Precalculus Enhanced with Graphing Utilities (7th Edition)
University Calculus: Early Transcendentals (4th Edition)
Precalculus (10th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
- The efficiency of an internal combustion engine is given below, where v1/v2 is the ratio of the uncompressed gas to the compressed gas and c is a positive constant dependent on the engine design. Efficiency (%) = 100[1 − 4/(v1/v2)c] Find the limit of the efficiency as the compression ratio approaches infinity.arrow_forwardevaluate (a) lim x→ x^2 - 36/x^2 + 5x - 6 (b) the demand curve of a firm is p= -10q + 5900 and its average cost is A(q) = 2q^2 - 4q + 140 + 845/q. where q is the firm's output produced and sold. 1. derive an expression for the total revenue of the firm. 2. derive an expression for the firm's total profit function 3. derive an expression for the rate of change of profit function of the firm. 4. is the rate of change of profit increasing or decreasing when the firm's output level is q= 50? 5. determine the level of output for which the total profit of the firm is maximized 6. what is the firm's maximum profitarrow_forwardShow that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.) Solve the constraint for y. y = ? Substitute into f. f(x,y)= ? Determine the behavior of f as x approaches −∞. limx→−∞f(x,y)= ? Determine the behavior of f as x approaches ∞. limx→∞f(x,y)= ? Does this show that f does not have an absolute maximum or minimum? 1. No 2. Yesarrow_forward
- lim y approaches 2 .............. y + 2/[y^2 + 5y + 6]arrow_forward12. Consider that the inflation rate in a six-year period in Mexico behaves according to the function i(T)=t^2 - t + 3Calculate the minimum value of inflation and the time in which it reaches this value. Consider the domain of the function [0,6] and the time in years. Provide the graphic behavior of inflation during the six-year period.In what interval does I(+) decrease? That is, there is deflation.arrow_forward(a) Find the following: i. Lim →x/ + 9x/ 6x/ − 4x/ii. Lim →(2x − 1)/ − 3 x − 5(b) The total revenue curve of a firm is R(q) = 40q − 12q and its average cost A(q) =1 30q − 12.85q + 20 +400 q,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?arrow_forward
- limit as x→−∞ 4/(e^x+7)=0 Enter the left-hand asymptote: y=arrow_forward1.Identify the kind of function. 2.Find the x- and y- intercepts and the vertical abs horizontal asymptotes. 3.Find the end behavior of the function (y,y)arrow_forward1. Evaluate lim (2x-5) given its graph below. x →2 a.0 b. -1 c. 2 d. 1 2. Given the graph of f(x) below, evaluate its limit as x approaches 3. a.2 b. 3 c. 1 d. 0arrow_forward
- Use the graph of the function h(x) given below to answer the questions that follow. (1) Evaluate h(2). 2 DNE 4 (a) Find lim x → 2- h(x) (b) Find lim x → 2+ h(x) (c) Use your answers from parts (b) and (c) to find lim x → 2 h(x)arrow_forward(a) for g(t)= t-9/square root t-3 . Make table of values with at least six appropriate inputs to evaluate the limits as t tends to 9. (b) make a conjecture about the value of lim t-9/square root t-3. t->9arrow_forwardIn an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point followed by a maximum, so a cubic model may be appropriate. In this exercise we use the model shown below, with n measured in thousands of units of input and T measured in thousands of units of product. T = −2n3 + 3n2 + n (a) Make a graph of T as a function of n. Include values of n up to 1.5 thousand units. (b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.)T( )Calculate that value. (Round your answer to two decimal places.) thousand units(c) Find the approximate location of the inflection point. (Round…arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning