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Chapter 3 Solutions
Applied Calculus
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Calculus and Its Applications (11th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus: Mathematics for Calculus - 6th Edition
University Calculus: Early Transcendentals (3rd Edition)
- . f (x) = x^2 +2 x<3 10 x=3 -3+4x x>3 1. At what value is this function discontinuous, if any? What is the lim f (x) 3 ? What is the lim f (x) 1? d. What is the value of f (4) ?arrow_forwardThe 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_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
- True or False? b). If lim x -> 5f(x) = DNE, then f (5) =DNE.If the statement is TRUE, explain why. If the statement is FALSE, sketch the graph of a counterexample.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_forwardFind the function f whose graph is given, state the value of the given quantity if it exists. If answer does not exist enter DNE A) lim f(x) X->2- B) lim f(x) X->2+ C) lim f(x) X->2 D) lim f (x) X->9 E) f(9)arrow_forward
- Question content area top Part 1 By determining f′(x)=limh→0f(x+h)−f(x)h, find f′(6) for the given function. f(x)=7x2arrow_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_forwarda)Find the domain of the function f and graph the domain of f. b) Show that lim (x,y) —>(0,1) f (x, y) cannot be found.arrow_forward
- A patient receives a 150-mg injection of a drug every 4 hours. The graph shows the amount f(t) of the drug in the bloodstream Find after t hours Find lim F(t) and lim f(t) t->4− t-> 4+ lim f(t) = mg t → 4− lim f(t) = mg t → 4+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_forwardUse the graph of the function h(x) given below to answer the questions that follow. (1) Evaluate h(−2) (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
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning