8. The logistic model is important in the modelling of population dynamics and is represented by1. For the following functions determine the following limits (if they exist):(i) lim7³–5x+37(ii) limr+1(iii) lim 9-5(iv) limN(t) =1+ (* - 1).e-akt(v) lim 2r+1(vi) lim r-2(vii) lim +3||z-322+z-6(viii) lim v25-z-3z4 -16whereN(t) is the population at some time t (days)2. For the function f(x) defined byNo = N(0) is the initial populationO if x is an integerf(x) =a and k are positive constants1 if æ is not an integer• At t =0 the population is 5(a) Sketch the graph of y = f(æ) for x € [-4,4]• At one week (t = 7) the population is 10(b) Find lim f(æ) (if it does not exist, explain why it is the case).• Eventually after a long time the population is 1003. Given the following functions find the limits (if they exist).If the function is discontinuous state(a) Given these three pieces of information provided about the model, find the exact values of No, athe type of discontinuity:and k.(i) lim,교_ir+4-4r +1,x 21(b) What is the approximate value of N after two weeks?(ii) lim f(x) where f(x) = «-1,I < 1(c) Approximately after what time was N= 50?(iii) limI--3-32 (z²+6z+9)(z+3)²(d) Sketch the graph of N(t) (labelling all axes,asymptotes and intercepts).3x + c,T< -1(iv) Find the value of c such that f(x) =is continuous5+ 4r3,x > -14. For functions F(r) =8z2+20r-124r²+4x–3(a) Completely factorise the numerator(b) Completely factorise the denominator(c) Find the coordinates of any "holes" in the graph of the function (removable discontinuities)(d) Find all æ- and y, intercepts fr the function(e) By using the polynomial division algorithm re-express the function is asymptote form(f) Find all asymptotes for F(r)(g) State the domain and range of F(h) Explain the asymptotic behaviour of F (by asymptotic behaviour this means somethinglike "as a → x, f(x) → 2")(i) Carefully sketch the graph of y = F(x) including all the information found in parts (a)-(h).5. (a) Simplify –5 (xy¬1)¯° in a form such that all exponents are positive integers.(b) Solve z22" = x2*+1 for r(c) Solve 13"-27L = 0.for r(d) Solve 25* – 26(5*) + 25 = 0 for r(e) For f(x) = V , find dom(f)6. Solve for a with each of the following:(i) (32)³z+1(ii) log5(4x – 3) = log3 (9)(a) (iii) 9 ()° = 4 + 2 (4)ª(iv) 3 (8-ª) = } (72z+1)(v) 2 log2r+1 (2x + 4) – log2r+1 (4) = 2= 1287. (a) Exactly calculate ?log4 8log, 2(b) Write In (V2x + 1) + ln(x) – In(|sin æ|) in one expression.(c) Solve for r : log2 () = 4(d) Beginning with f(x) = In(x), sketch the sequence of transformations such that f(x) =3 In(4 – a) + 2(e) Find dom(f) and ran(f) for f(x) =VIn(2r+1)

As many questions are given , I will solve the first Question (3 parts) We have to evaluate the…

Answered: 1. For the following functions…

1. For the following functions determine the following limits (if they exist): (i) lim =-5e+3 (iii) lim (ii) _lim (iv) lim +2

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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