Concept explainers
SAT Scores by Income The following bar graph shows U.S. math SAT scores as a function of household income:8
These data can be modeled by
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Finite Mathematics and Applied Calculus (MindTap Course List)
- a) lim f(x) x→0^- b) lim f(x) x→0^+ c) lim f(x) x→0 d) lim f(x) x→2^- e) lim f(x)…arrow_forward[3 - x x 2 let fx)=+1 a) Find lim fx) and lim f) X-2 X-2+ exist? why? Sx) b) Dose lim X2arrow_forwardTrue or False? b). If f(4) = 9, then it must be true that lim(x->4) f(x)= 0 If the statement is TRUE, explain why. If the statement is FALSE, sketch the graph of a counterexample.arrow_forward
- lim g(f(x))x->-2arrow_forward(a) What is wrong with the following equation? x2 + x − 12 x − 3 = x + 4 (x − 3)(x + 4) ≠ x2 + x − 12 The left-hand side is not defined for x = 0, but the right-hand side is. The left-hand side is not defined for x = 3, but the right-hand side is.None of these — the equation is correct. (b) In view of part (a), explain why the equation lim x → 3 x2 + x − 12 x − 3 = lim x → 3 (x + 4) is correct. Since x2 + x − 12 x − 3 and x + 4 are both continuous, the equation follows. Since the equation holds for all x ≠ 3, it follows that both sides of the equation approach the same limit as x → 3. This equation follows from the fact that the equation in part (a) is correct.None of these — the equation is not correct.arrow_forwardUse the formula below to find the instantaneous rate of change of the function at the given x-value. f(x) = 3x2 + x − 5 at x = 5 Average and Instantaneous Rate of Change▲ The average rate of change of a function f between x and x + h is f(x + h) − f(x) h . (Difference quotient gives the average rate of change.) The instantaneous rate of change of a function f at the number x is lim h→0 f(x + h) − f(x) h (Taking the limit makes it instantaneous.)arrow_forward
- Find lim x → 0 e* + 1 x² + 4 Answer only please (NB * is x )arrow_forwardGiven lim (4x-3) as x approaches 1. Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08arrow_forwardSales of a new model of compact disc player are approximated by the function S(x) = 1000 - 800e-x, where S(x) is in appropriate units and x represents the number of years the disc player has been on the market.(a) Find the sales during year 0.(b) In how many years will sales reach 500 units?(c) Will sales ever reach 1000 units?(d) Is there a limit on sales for this product? If so, what is it?arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning