6 Question 6Which statement(s) is(are) true?(1) f(x) = |x is differentiable at 0.1(ii) f(x) == is differentiable at 0.() [f(x) g(x²)] = f'(x) · g(x²) + f(x) · g(x²).O (i), (ii), and (iii)(iii) onlyO (i) only(ii) onlyNone of the statements are true.

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Answered: Which statement(s) is(are) true? (1)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 40E

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Decay 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.
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Question 1 Some values of a differentiable, invertible function fand its derivative are given below.x0 2 4 6 8f(x) 15 13 10 6 2f′(x) −1 −2 −2.5 −3 −5 Calculate the following.(a) g′(2), where g(x) = f(x)e3x.(b) h′(6), where h(x) = xef(x). Question 2 Use the table below to evaluate the derivatives below.xf(x) f′(x) g(x) g′(x) h(x) h′(x)1 2 3 4 5 −2 −1 (a) Let F(x) = f(x)g(x) and find F′(1).(b) Let G(x) = g(x)f(x) and find G′(1).(c) Let H(x) = f(x)g(x)h(x) and find H′(1).(d) Let J(x) = f(x)g(x)h(x) and find J′(1). Question 3 A mass is hanging from the ceiling on a spring and oscillating (forever, and without friction). At itshighest point, the mass is 12 cm from the floor, and at its lowest point, the mass is 6 cm from thefloor. At t= 0, the mass is at its equilibrium and moving downwards, and a single period takes 0.5seconds. HINT: Graph your y(t) to check your answers. (a) Find a formula for y(t), the position of the mass from the floor as a function of time.(b) What is the position,…

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Which statement(s) is(are) true? (1) f(x)= |a| is differentiable at 0. is differentiable at 0. () [f(x) 9 (x²)] = f'(x) · g(x²) + f(x) · g(x²) (i), (ii), and (iii) (iii) only O (i) only (ii) only None of the statements are true.