1 Limits And Continuity 2 The Derivative 3 Topics In Differentiation 4 The Derivative In Graphing And Applications 5 Integration 6 Applications Of The Definite Integral In Geometry, Science, And Engineering 7 Principles Of Integral Evaluation 8 Mathematical Modeling With Differential Equations 9 Infinite Series 10 Parametric And Polar Curves; Conic Sections 11 Three-dimensional Space; Vectors 12 Vector-valued Functions 13 Partial Derivatives 14 Multiple Integrals 15 Topics In Vector Calculus expand_more
4.1 Analysis Of Functions I: Increase, Decrease, And Concavity 4.2 Analysis Of Functions Ii: Relative Extrema; Graphing Polynomials 4.3 Analysis Of Functions Iii: Rational Functions, Cusps, And Vertical Tangents 4.4 Absolute Maxima And Minima 4.5 Applied Maximum And Minimum Problems 4.6 Rectilinear Motion 4.7 Newton’s Method 4.8 Rolle’s Theorem; Mean-value Theorem Chapter Questions expand_more
Problem 1QCE: A positive number x and its reciprocal are added together. The smallest possible value of this sum... Problem 2QCE: Two nonnegative numbers, x and y, have a sum equal to 10 . The largest possible product of the two... Problem 3QCE: A rectangle in the xy-plane has one comer at the origin, an adjacent comer at the point x,0, and a... Problem 4QCE: An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by... Problem 1ES: Find a number in the closed interval 12,32 such that the sum of the number and its reciprocal is (a)... Problem 2ES: How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is... Problem 3ES: A rectangular field is to be bounded by a fence on three sides and by a straight stream on the... Problem 4ES: The boundary of a field is a right triangle with a straight stream along its hypotenuse and with... Problem 5ES: A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will... Problem 6ES: A rectangle is to be inscribed in a right triangle having sides of length 6in,8in, and 10in . Find... Problem 7ES: Solve the problem in Exercise 6 assuming the rectangle is positioned as in Figure Ex-7. Problem 8ES: A rectangle has its two lower comers on the x-axis and its two upper comers on the curve y=16x2 .... Problem 9ES: Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius... Problem 10ES: Find the point P in the first quadrant on the curve y=x2 such that a rectangle with sides on the... Problem 11ES: A rectangular area of 3200ft2 is to be fenced off. Two opposite sides will use fencing costing $1... Problem 12ES: Show that among all rectangles with perimeter p, the square has the maximum area. Problem 13ES: Show that among all rectangles with area A, the square has the minimum perimeter. Problem 14ES: A wire of length 12in can be bent into a circle, bent into a square, or cut into two pieces to make... Problem 15ES: A rectangle R in the plane has comers at 8,12, and a 100 by 100 square S is positioned in the plane... Problem 16ES: Solve the problem in Exercise 15 if S is a 16 by 16 square. Problem 17ES: Solve the problem in Exercise 15 if S is positioned with its lower left comer on the line y=6x . Problem 18ES: A rectangular page is to contain 42 square inches of printable area. The margins at the top and... Problem 19ES: A box with a square base is taller than it is wide. In order to send the box through the U.S. mail,... Problem 20ES: A box with a square base is wider than it is tall. In order to send the box through the U.S. mail,... Problem 21ES: An open box is to be made from a 3ft by 8ft rectangular piece of sheet metal by cutting out squares... Problem 22ES: A closed rectangular container with a square base is to have a volume of 2250in3 . The material for... Problem 23ES: A closed rectangular container with a square base is to have a volume of 2000cm3 . It costs twice as... Problem 24ES: A container with square base, vertical sides, and open top is to be made from 1000ft2 of material.... Problem 25ES: A rectangular container with two square sides and an open top is to have a volume of V cubic units.... Problem 26ES: A church window consisting of a rectangle topped by a semicircle is to have a perimeter p . Find the... Problem 27ES: Find the dimensions of the right circular cylinder of largest volume that can be inscribed in a... Problem 28ES: Find the dimensions of the right circular cylinder of greatest surface area that can be inscribed in... Problem 29ES: A closed, cylindrical can is to have a volume of V cubic units. Show that the can of minimum surface... Problem 30ES: A closed cylindrical can is to have a surface area of S square units. Show that the can of maximum... Problem 31ES: A cylindrical can, open at the top, is to hold 500cm3 of liquid. Find the height and radius that... Problem 32ES: A soup can in the shape of a right circular cylinder of radius r and height h is to have a... Problem 33ES: A box-shaped wire frame consists of two identical wire squares whose vertices are connected by four... Problem 34ES: Suppose that the sum of the surface areas of a sphere and a cube is a constant. (a) Show that the... Problem 35ES: Find the height and radius of the cone of slant height L whose volume is as large as possible. Problem 36ES: A cone is made from a circular sheet of radius R by cutting out a sector and gluing the cut edges of... Problem 37ES: A cone-shaped paper drinking cup is to hold 100cm3 of water. Find the height and radius of the cup... Problem 38ES: Find the dimensions of the isosceles triangle of least area that can be circumscribed about a circle... Problem 39ES: Find the height and radius of the right circular cone with least volume that can be circumscribed... Problem 40ES: A commercial cattle ranch currently allows 20 steers per acre of grazing land; on the average its... Problem 41ES Problem 42ES: A fertilizer producer finds that it can sell its product at a price of p=3000.1x dollars per unit... Problem 43ES: (a) A chemical manufacturer sells sulfuric acid in bulk at a price of $100 per unit. If the daily... Problem 44ES: A firm determines that x units of its product can be sold daily at p dollars per unit, where x=1000p... Problem 45ES: In a certain chemical manufacturing process, the daily weight y of defective chemical output depends... Problem 46ES: An independent truck driver charges a client $15 for each hour of driving, plus the cost of fuel. At... Problem 47ES: A trapezoid is inscribed in a semicircle of radius 2 so that one side is along the diameter (Figure... Problem 48ES: A drainage channel is to be made so that its cross section is a trapezoid with equally sloping sides... Problem 49ES: A lamp is suspended above the center of a round table of radius r . How high above the table should... Problem 50ES: A plank is used to reach over a fence 8ft high to support a wall that is 1ft behind the fence... Problem 51ES: Two particles, A and B, are in motion in the xy-plane . Their coordinates at each instant of time... Problem 52ES: Follow the directions of Exercise 51, with xA=t,yA=t2,xB=2t, and yB=2 . Problem 53ES: Find the coordinates of the point P on the curve y=1x2x0 where the segment of the tangent line at P... Problem 54ES: Find the x-coordinate of the point P on the parabola y=1x20x1 where the triangle that is enclosed by... Problem 55ES: Where on the curve y=1+x21 does the tangent line have the greatest slope? Problem 56ES: Suppose that the number of bacteria in a culture at time t is given by N=500025+tet/20 . (a) Find... Problem 57ES: The shoreline of Circle Lake is a circle with diameter 2mi . Nancy’s training routine begins at... Problem 58ES: A man is floating in a rowboat 1 mile from the (straight) shoreline of a large lake. A town is... Problem 59ES: A pipe of negligible diameter is to be carried horizontally around a comer from a hallway 8ft wide... Problem 60ES: A concrete barrier whose cross section is an isosceles triangle runs parallel to a wall. The height... Problem 61ES: Suppose that the intensity of a point light source is directly proportional to the strength of the... Problem 62ES: Given points A2,1 and B5,4, find the point P in the interval 2,5 on the x-axis that maximizes angle... Problem 63ES: The lower edge of a painting, 10ft in height, is 2ft above an observer’s eye level. Assuming that... Problem 64ES: Fermat’s principle (biography on p.213 ) in optics states that light traveling from one point to... Problem 65ES: Fermat’s principle (Exercise 64) also explains why light rays traveling between air and water... Problem 66ES: A farmer wants to walk at a constant rate from her bam to a straight river, fill her pail, and carry... Problem 67ES Problem 68ES: Prove: If fx0 on an interval and if fx has a maximum value on that interval at x0, then fx also has... format_list_bulleted
Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning