Linear approximation Find the linear approximation to the following functions at the given point a.
27.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus (10th Edition)
Precalculus
Calculus: Early Transcendentals (2nd Edition)
- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?arrow_forwardDecay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forwardHollings Functional Response Curve The total number P of prey taken by a predator depends on the availability of prey. C.S. Holling proposed a function of the form P=cn(1+dn) to model the number of prey taken in certain situations. Here n is the density of prey available, and c and d are constants that depend on the organisms involved as well as on other environmental features. Holling took data gathered earlier by T. Burnett on the number of sawfly cocoons found by a small wasp parasite at given host density. In one such experiment conducted, Holling found the relationship p=21.96n1+2.41n, Where P is the number of cocoons parasitized and n is the density of cocoons available measured as number per square inch. a Draw a graph of p versus n. Include values of n up to 2 cocoons per square inch. b What density of cocoons will ensure that the wasp will find and parasitize 6 of them? c There is a limit to the number of cocoons that the wasp is able to parasitize no matter how readily available the prey may be. What is this upper limit?arrow_forward
- The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b.What is the cost of making 25 items? c.Suppose the maximum cost allowed is SI500. What are the domain and range of the cost function, C(x) ?arrow_forwardbThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning