Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
10th Edition
ISBN: 9781305657861
Author: Soo T. Tan
Publisher: Cengage Learning
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Chapter 8.8, Problem 13E
To determine
To find: The volume of the solid bounded by the surface
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Each of the following statements is an attempt to show that a given series is convergent or
divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C
(for "correct") if the argument is valid, or enter | (for "incorrect") if any part of the argument is
flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.)
☐ 1. For all n > 1,
seriesΣ In(n)
In(n)
converges.
2, 1,
arctan(n)
the series arctan(n)
n³
☐ 4. For all n > 1,
123
converges.
1
n ln(n)
series In(n) diverges.
2n
.
and the seriesΣconverges, so by the Comparison Test,
2, 3, and the series converges, so by the Comparison Test, the
series-3
1
converges.
☐ 6. For all n > 2, In(n) >, and the series Σ converges, so by the Comparison Test, the
seriesΣ
In(n) converges.
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Chapter 8 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
Ch. 8.1 - What is a function of two variables? Give an...Ch. 8.1 - Prob. 2CQCh. 8.1 - Prob. 3CQCh. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.1 - Let f(x, y) = x2+ 2xy x + 3. Compute f(1, 2),...Ch. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Let h(s, t) = s ln t t ln s. Compute h(1, e),...
Ch. 8.1 - Prob. 8ECh. 8.1 - Let g(r, s, t) = res/t. Compute g(1, 1, 1), g(1,...Ch. 8.1 - Prob. 10ECh. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 14ECh. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 16ECh. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - In Exercises 19-24, sketch the level curves of the...Ch. 8.1 - Prob. 22ECh. 8.1 - In Exercises 1924, sketch the level curves of the...Ch. 8.1 - Prob. 24ECh. 8.1 - Find an equation of the level curve of f (x, y) =...Ch. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - POISEITLLES LAW Poiseuilles Law states that the...Ch. 8.1 - COST FUNCTION FOR A LOUDSPEAKER SYSTEM Acrosonic...Ch. 8.1 - Prob. 38ECh. 8.1 - REVENUE FUNCTIONS FOR DESKS Country Workshop...Ch. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - Prob. 61ECh. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.2 - Prob. 1CQCh. 8.2 - Prob. 2CQCh. 8.2 - Prob. 3CQCh. 8.2 - Prob. 4CQCh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - In Exercises 3-24, find the first partial...Ch. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - PROFIT FUNCTIONS The monthly profit (in dollars)...Ch. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Prob. 59ECh. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Prob. 63ECh. 8.2 - Prob. 64ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.2 - Prob. 68ECh. 8.2 - Prob. 69ECh. 8.2 - Prob. 70ECh. 8.2 - Prob. 72ECh. 8.2 - Prob. 1TECh. 8.2 - Prob. 2TECh. 8.2 - Prob. 3TECh. 8.2 - Prob. 4TECh. 8.2 - Prob. 5TECh. 8.2 - Prob. 6TECh. 8.3 - Explain the terms (a) relative maximum of a...Ch. 8.3 - Prob. 2CQCh. 8.3 - Prob. 3CQCh. 8.3 - Prob. 4CQCh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - In Exercises 1-20, find the critical point(s) of...Ch. 8.3 - In Exercises 1-20, find the critical point(s) of...Ch. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Prob. 17ECh. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - MAXIMIZATION PROFIT The total weekly revenue (in...Ch. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.3 - MAXIMIZING REVENUE The management of Cal...Ch. 8.3 - Prob. 26ECh. 8.3 - MAXIMIZING PROFIT Johnsons Household Products has...Ch. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Prob. 40ECh. 8.3 - Prob. 41ECh. 8.3 - Prob. 42ECh. 8.4 - Explain the terms (a) scatter diagram and (b)...Ch. 8.4 - Prob. 2CQCh. 8.4 - Prob. 4CQCh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - In Exercises 16, (a) find an equation of the...Ch. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - COLLEGE ADMISSIONS The following data, compiled by...Ch. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8.4 - Prob. 27ECh. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Prob. 1TECh. 8.4 - Prob. 2TECh. 8.4 - Prob. 3TECh. 8.4 - Prob. 4TECh. 8.4 - Prob. 5TECh. 8.4 - Prob. 6TECh. 8.4 - Prob. 7TECh. 8.4 - Prob. 8TECh. 8.4 - Prob. 9TECh. 8.5 - What is a constrained relative extremum of a...Ch. 8.5 - Prob. 2CQCh. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 9ECh. 8.5 - Prob. 10ECh. 8.5 - In Exercises 1-16. use the method of Lagrange...Ch. 8.5 - Prob. 12ECh. 8.5 - In Exercises 1-16. use the method of Lagrange...Ch. 8.5 - Prob. 14ECh. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - MAXIMIZING PROFIT The total weekly profit (in...Ch. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - PACKAGING Find the dimensions of an open...Ch. 8.5 - Prob. 22ECh. 8.5 - Prob. 23ECh. 8.5 - Prob. 24ECh. 8.5 - MINIMIZING CONTAINER COSTS The Betty Moore Company...Ch. 8.5 - Prob. 26ECh. 8.5 - Prob. 27ECh. 8.5 - Prob. 28ECh. 8.5 - Prob. 29ECh. 8.5 - Prob. 30ECh. 8.5 - Prob. 31ECh. 8.5 - Prob. 33ECh. 8.5 - Prob. 34ECh. 8.5 - Prob. 36ECh. 8.5 - Prob. 38ECh. 8.5 - Prob. 39ECh. 8.5 - Prob. 40ECh. 8.5 - Prob. 41ECh. 8.5 - Prob. 42ECh. 8.6 - Prob. 1CQCh. 8.6 - Prob. 2CQCh. 8.6 - Prob. 1ECh. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - Prob. 5ECh. 8.6 - Prob. 6ECh. 8.6 - Prob. 7ECh. 8.6 - Prob. 8ECh. 8.6 - Prob. 9ECh. 8.6 - Prob. 10ECh. 8.6 - Prob. 11ECh. 8.6 - Prob. 12ECh. 8.6 - Prob. 13ECh. 8.6 - Prob. 14ECh. 8.6 - In Exercises 318, find the total differential of...Ch. 8.6 - Prob. 16ECh. 8.6 - Prob. 17ECh. 8.6 - Prob. 18ECh. 8.6 - Prob. 19ECh. 8.6 - Prob. 20ECh. 8.6 - Prob. 21ECh. 8.6 - Prob. 22ECh. 8.6 - Prob. 23ECh. 8.6 - Prob. 24ECh. 8.6 - Prob. 25ECh. 8.6 - Prob. 26ECh. 8.6 - Prob. 27ECh. 8.6 - Prob. 28ECh. 8.6 - Prob. 29ECh. 8.6 - Prob. 30ECh. 8.6 - Prob. 31ECh. 8.6 - Prob. 32ECh. 8.6 - Prob. 33ECh. 8.6 - Prob. 34ECh. 8.6 - Prob. 35ECh. 8.6 - Prob. 36ECh. 8.6 - Prob. 37ECh. 8.6 - Prob. 38ECh. 8.6 - Prob. 39ECh. 8.6 - Prob. 40ECh. 8.6 - Prob. 41ECh. 8.6 - Prob. 42ECh. 8.6 - Prob. 43ECh. 8.6 - Prob. 44ECh. 8.6 - Prob. 45ECh. 8.6 - Prob. 46ECh. 8.6 - Prob. 47ECh. 8.6 - Prob. 48ECh. 8.7 - Prob. 1CQCh. 8.7 - Prob. 2CQCh. 8.7 - Prob. 3CQCh. 8.7 - Prob. 4CQCh. 8.7 - Prob. 1ECh. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - Prob. 9ECh. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - Prob. 14ECh. 8.7 - Prob. 15ECh. 8.7 - Prob. 16ECh. 8.7 - Prob. 17ECh. 8.7 - Prob. 18ECh. 8.7 - In Exercises 1-25. evaluate the double integral...Ch. 8.7 - Prob. 20ECh. 8.7 - Prob. 21ECh. 8.7 - Prob. 22ECh. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Prob. 25ECh. 8.7 - Prob. 26ECh. 8.7 - Prob. 27ECh. 8.8 - Prob. 1CQCh. 8.8 - Prob. 2CQCh. 8.8 - Prob. 3CQCh. 8.8 - Prob. 1ECh. 8.8 - Prob. 2ECh. 8.8 - Prob. 3ECh. 8.8 - Prob. 4ECh. 8.8 - Prob. 5ECh. 8.8 - Prob. 6ECh. 8.8 - Prob. 7ECh. 8.8 - Prob. 8ECh. 8.8 - Prob. 9ECh. 8.8 - Prob. 10ECh. 8.8 - Prob. 11ECh. 8.8 - Prob. 12ECh. 8.8 - Prob. 13ECh. 8.8 - Prob. 14ECh. 8.8 - Prob. 15ECh. 8.8 - Prob. 16ECh. 8.8 - Prob. 17ECh. 8.8 - Prob. 18ECh. 8.8 - Prob. 19ECh. 8.8 - Prob. 20ECh. 8.8 - Prob. 21ECh. 8.8 - Prob. 22ECh. 8.8 - Prob. 23ECh. 8.8 - Prob. 24ECh. 8.8 - Prob. 25ECh. 8.8 - Prob. 26ECh. 8.8 - Prob. 27ECh. 8.8 - Prob. 28ECh. 8.8 - Prob. 29ECh. 8 - Prob. 1CRQCh. 8 - Prob. 2CRQCh. 8 - Prob. 3CRQCh. 8 - Prob. 4CRQCh. 8 - Prob. 5CRQCh. 8 - Prob. 6CRQCh. 8 - Prob. 7CRQCh. 8 - Prob. 8CRQCh. 8 - Prob. 9CRQCh. 8 - Prob. 10CRQCh. 8 - Prob. 11CRQCh. 8 - Prob. 12CRQCh. 8 - Prob. 13CRQCh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RECh. 8 - Prob. 62RECh. 8 - Prob. 1BMCh. 8 - Prob. 2BMCh. 8 - Prob. 3BMCh. 8 - Prob. 4BMCh. 8 - Prob. 5BMCh. 8 - Prob. 6BMCh. 8 - Prob. 7BM
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- Question 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final…arrow_forwardQuestion 3: A sealed flask at room temperature contains a mixture of neon (Ne) and nitrogen (N2) gases. Ne has a mass of 3.25 g and exerts a pressure of 48.2 torr. . N2 contributes a pressure of 142 torr. • What is the mass of the N2 in the flask? • Atomic mass of Ne = 20.1797 g/mol • Atomic mass of N = 14.0067 g/mol Solution: We will use the Ideal Gas Law to determine the number of moles of each gas and calculate the mass of N2. PV = nRT where: • P = total pressure • V volume of the flask (same for both gases) n = number of moles of gas • R 0.0821 L atm/mol K • T = Room temperature (assume 298 K) Since both gases are in the same flask, their partial pressures correspond to their mole fractions. Step 1: Convert Pressures to Atmospheres 48.2 PNe = 0.0634 atm 760 142 PN2 = = 0.1868 atm 760 Step 2: Determine Moles of Ne nNe = mass molar mass 3.25 nNe 20.1797 nne 0.1611 mol Step 3: Use Partial Pressure Ratio to Find narrow_forward"I have written solutions in text form, but I need experts to rewrite them in handwriting from A to Z, exactly as I have written, without any changes."arrow_forward
- 3.12 (B). A horizontal beam AB is 4 m long and of constant flexural rigidity. It is rigidly built-in at the left-hand end A and simply supported on a non-yielding support at the right-hand end B. The beam carries Uniformly distributed vertical loading of 18 kN/m over its whole length, together with a vertical downward load of 10KN at 2.5 m from the end A. Sketch the S.F. and B.M. diagrams for the beam, indicating all main values. Cl. Struct. E.] CS.F. 45,10,376 KN, B.M. 186, +36.15 kNm.7arrow_forwardQize f(x) = x + 2x2 - 2 x² + 4x²² - Solve the equation using Newton Raphsonarrow_forward-b±√√b2-4ac 2a @4x²-12x+9=0 27 de febrero de 2025 -b±√√b2-4ac 2a ⑥2x²-4x-1=0 a = 4 b=-12 c=9 a = 2 b = 9 c = \ x=-42±√(2-4 (4) (9) 2(4)) X = (12) ±√44)-(360) 2(108) x = ±√ X = =±√√²-4(2) (1) 2() X = ±√ + X = X = + X₁ = = X₁ = X₁ = + X₁ = = =arrow_forward
- 3.9 (A/B). A beam ABCDE, with A on the left, is 7 m long and is simply supported at Band E. The lengths of the various portions are AB 1-5m, BC = 1-5m, CD = 1 m and DE : 3 m. There is a uniformly distributed load of 15kN/m between B and a point 2m to the right of B and concentrated loads of 20 KN act at 4 and 0 with one of 50 KN at C. (a) Draw the S.F. diagrams and hence determine the position from A at which the S.F. is zero. (b) Determine the value of the B.M. at this point. (c) Sketch the B.M. diagram approximately to scale, quoting the principal values. [3.32 m, 69.8 KNm, 0, 30, 69.1, 68.1, 0 kNm.]arrow_forward4. Verify that V X (aẢ) = (Va) XẢ + aV X Ả where Ả = xyz(x + y + 2) A and a = 3xy + 4zx by carrying out the detailed differentiations.arrow_forward3. For each of the arrow or quiver graphs shown below, determine analytically V°C and V X Č. From these analytical solutions, identify the extrema (+/-) and plot these points on the arrow graph. (a) C = −✰CosxSiny + ŷSinxCosy -π<ׂу<π Ty (b) C = −xSin2y + ŷCos2y x, y<π -π< (c) C = −xCosx + ŷSiny -π< x, y < πarrow_forward
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