P Preparation For Calculus 1 Limits And Their Properties 2 Differentiation 3 Applications Of Differentiation 4 Integration 5 Logarithmic, Exponential, And Other Transcendental Functions 6 Differential Equations 7 Applications Of Integration 8 Integration Techniques, L’hopital’s Rule, And Improper Integrals 9 Infinite Series 10 Conics, Parametric Equations, And Polar Coordinates 11 Vectors And The Geometry Of Space 12 Vector-valued Functions 13 Functions Of Several Variables 14 Multiple Integration 15 Vector Analysis expand_more
3.1 Extrema On An Interval 3.2 Rolle’s Theorem And The Mean Value Theorem 3.3 Increasing And Decreasing Functions And The First Derivative Test 3.4 Concavity And The Second Derivative Test 3.5 Limits At Infinity 3.6 A Summary Of Curve Sketching 3.7 Optimization Problems 3.8 Newton’s Method 3.9 Differentials Chapter Questions expand_more
Problem 1RE: Finding Extrema on a Closed Interval In Exercises 1-8, Find the absolute extrema of the function on... Problem 2RE: Finding Extrema on a Closed Interval In Exercises 1-8, find the absolute extrema of the function on... Problem 3RE Problem 4RE Problem 5RE Problem 6RE Problem 7RE Problem 8RE Problem 9RE Problem 10RE Problem 11RE Problem 12RE Problem 13RE Problem 14RE Problem 15RE Problem 16RE Problem 17RE Problem 18RE Problem 19RE Problem 20RE Problem 21RE Problem 22RE Problem 23RE Problem 24RE Problem 25RE Problem 26RE Problem 27RE Problem 28RE: Applying the First Derivative Test In Exercises 27-34, (a) find the critical numbers of f, if any,... Problem 29RE Problem 30RE Problem 31RE Problem 32RE: Applying the First Derivative Test In Exercises 27-34, (a) find the critical numbers of f, if any,... Problem 33RE Problem 34RE Problem 35RE Problem 36RE Problem 37RE Problem 38RE Problem 39RE Problem 40RE Problem 41RE Problem 42RE Problem 43RE Problem 44RE Problem 45RE Problem 46RE: Using the Second Derivative Test In Exercises 4348, find all relative extrema of the function. Use... Problem 47RE Problem 48RE Problem 49RE Problem 50RE Problem 51RE Problem 52RE: Modeling Data The manager of a store recorded the annual sales S (in thousands of dollars) of a... Problem 53RE Problem 54RE Problem 55RE Problem 56RE Problem 57RE Problem 58RE Problem 59RE Problem 60RE Problem 61RE Problem 62RE Problem 63RE Problem 64RE Problem 65RE: Horizontal Asymptotes In Exercises 6366, use a graphing utility to graph the function and identify... Problem 66RE Problem 67RE Problem 68RE Problem 69RE Problem 70RE Problem 71RE Problem 72RE Problem 73RE Problem 74RE Problem 75RE Problem 76RE Problem 77RE: Maximum Area A rancher has 400 feet of fencing with which to enclose two adjacent rectangular... Problem 78RE: Maximum Area Find the dimensions of the rectangle of maximum area, with sides parallel to the... Problem 79RE Problem 80RE: Minimum Length The wall of a building is to be braced by a beam that must pass over a parallel fence... Problem 81RE Problem 82RE Problem 83RE Problem 84RE Problem 85RE Problem 86RE Problem 87RE Problem 88RE Problem 89RE Problem 90RE Problem 91RE Problem 92RE Problem 93RE Problem 94RE Problem 95RE Problem 96RE Problem 1PS: Relative Extrema Graph the fourth-degree polynomial p(x)=x4=ax2+1 for various values of the constant... Problem 2PS: Relative Extrema (a) Graph the fourth-degree polynomial p(x)=ax46x2 for a=3,2,1,0,1,2, and 3. For... Problem 3PS: Relative Minimum Let f(x)=cx+x2 Determine all values of the constant c such that f has a relative... Problem 4PS: Points of Inflection (a) Let f(x)=ax2+bx+c,a0, be a quadratic polynomial. How many points of... Problem 5PS: Extended Mean Value Theorem Prove the Extended Mean Value Theorem: If f and f are continuous on the... Problem 6PS: Illumination The amount of illumination of a surface is proportional to the intensity of the light... Problem 7PS: Minimum Distance Consider a room in the shape of a cube, 4 meters on each side. A bug at point P... Problem 8PS: Areas of Triangles The line joining P and Q crosses the two parallel lines, as shown in the figure.... Problem 9PS: Mean Value Theorem Determine the values a, b, and c such that the function f satisfies the... Problem 10PS: Mean Value Theorem Determine the values a. b, c. and d such that the function f satisfies the... Problem 11PS: Proof Let f and g be functions that are continuous on [a, b] and differentiable on (a, b). Prove... Problem 12PS: Proof (a) Prove that limxx2= (b) Prove that limx1x2=0 (c) Let L be a real number. Prove that if... Problem 13PS: Tangent Lines Find the point on the graph of y=11+x2 (see Figure) where the tangent line has the... Problem 14PS: Stopping Distance The police department must determine the speed limit on a bridge such that the... Problem 15PS: Darbouxs Theorem Prove Darbouxs Theorem: Let f be differentiable on the closed interval [a, b] such... Problem 16PS: Maximum Area The figures show a rectangle, a circle, and a semicircle inscribed in a triangle... Problem 17PS: Point of Inflection Show that the cubic polynomial p(x)=ax3+bx2+ca+d has exactly one point of... Problem 18PS: Minimum Length A legal-sized sheet of paper (8.5 inches by 14 inches) is folded so that comer P... Problem 19PS: Quadratic Approximation The polynomial P(x)=x0+c1(xa)+c2(xa)2 is the quadratic approximation of the... format_list_bulleted