Problem 1RCC: Explain the difference between an absolute maximum and a local maximum. Illustrate with a sketch. Problem 2RCC: (a) What does the Extreme Value Theorem say? (b) Explain how the Closed Interval Method works. Problem 3RCC: (a) State Fermats Theorem. (b) Define a critical number of f. Problem 4RCC: (a) State Rolles Theorem. (b) State the Mean Value Theorem and give a geometric interpretation. Problem 5RCC: (a) State the Increasing/Decreasing Test. (b) What does it mean to say that f is concave upward on... Problem 6RCC: (a) State the First Derivative Test. (b) State the Second Derivative Test. (c) What are the relative... Problem 7RCC: (a) What does lHospitals Rule say? (b) How can you use lHospitals Rule if you have a product f(x)... Problem 8RCC: State whether each of the following limit forms is indeterminate. Where possible, state the limit.... Problem 9RCC: If you have a graphing calculator or computer, why do you need calculus to graph a function? Problem 10RCC: (a) Given an initial approximation x1 to a root of the equation f(x) = 0, explain geometrically,... Problem 11RCC: (a) What is an antiderivative of a function f? (b) Suppose F1 and F2 are both antiderivatives of f... Problem 1RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 2RQ: If f has an absolute minimum value at c, then f(c) = 0. Problem 3RQ: If f is continuous on (a, b), then f attains an absolute maximum value f(c) and an absolute minimum... Problem 4RQ: If f is differentiable and f(1) f(1), then there is a number c such that | c | 1 and f(c) = 0. Problem 5RQ: If f(x) 0 for 1 x 6, then f is decreasing on (1, 6). Problem 6RQ: If f(2) = 0, then (2, f(2)) is an inflection point of the curve y = f(x). Problem 7RQ Problem 8RQ: There exists a function f such that f(1) = 2, f(3) = 0, and f(x) 1 for all x. Problem 9RQ Problem 10RQ: There exists a function f such that f(x) 0, f(x) 0, and f(x) 0 for all x. Problem 11RQ: If f and g are increasing on an interval I, then f + g is increasing on I. Problem 12RQ: If f and g are increasing on an interval I, then f g is increasing on I. Problem 13RQ: If f and g are increasing on an interval I, then fg is increasing on I. Problem 14RQ: If f and g are positive increasing functions on an interval I, then fg is increasing on I. Problem 15RQ: If f is increasing and f(x) 0 on I, then g(x) = 1/f(x) is decreasing on I. Problem 16RQ: If f is even, then f is even. Problem 17RQ Problem 18RQ Problem 19RQ: If f(x) exists and is nonzero for all x, then f(1) f(0). Problem 20RQ Problem 21RQ Problem 1RE: Find the local and absolute extreme values of the function on the given interval. f(x) = x3 9x2 +... Problem 2RE: Find the local and absolute extreme values of the function on the given interval. f(x)=x1x,[1,1] Problem 3RE Problem 4RE Problem 5RE: Find the local and absolute extreme values of the function on the given interval. f(x) = x + cos x,... Problem 6RE Problem 7RE: Evaluate the limit. limx0ex1tanx Problem 8RE Problem 9RE: Evaluate the limit. limx0e2xe2xln(x+1) Problem 10RE: Evaluate the limit. limxe2xe2xln(x+1) Problem 11RE: Evaluate the limit. limx(x2x3)e2x Problem 12RE Problem 13RE: Evaluate the limit. limx1+(xx11lnx) Problem 14RE: Evaluate the limit. limx(/2)(tanx)cosx Problem 15RE: Sketch the graph of a function that satisfies the given conditions. f(0) = 0, f(2) = f(l) = f(9) =... Problem 16RE: Sketch the graph of a function that satisfies the given conditions. f(0) = 0, f is continuous and... Problem 17RE: Sketch the graph of a function that satisfies the given conditions. f is odd, f(x) 0 for 0 x 2,... Problem 18RE Problem 19RE: Use the guidelines of Section 4.5 to sketch the curve. y = 2 2x x3 Problem 20RE: Use the guidelines of Section 4.5 to sketch the curve. y = 2x3 3x2 + 12x + 5 Problem 21RE: Use the guidelines of Section 4.5 to sketch the curve. y = 3x4 4x3 + 2 Problem 22RE Problem 23RE Problem 24RE Problem 25RE Problem 26RE Problem 27RE Problem 28RE Problem 29RE: Use the guidelines of Section 4.5 to sketch the curve. y = ex sin x, x Problem 30RE: Use the guidelines of Section 4.5 to sketch the curve. y = 4x tan x, /2 x /2 Problem 31RE Problem 32RE Problem 33RE Problem 34RE Problem 35RE Problem 36RE Problem 37RE Problem 38RE Problem 39RE Problem 43RE Problem 44RE: Investigate the family of functions f(x)=cxecx2. What happens to the maximum and minimum points and... Problem 45RE: Show that the equation 3x + 2 cos x + 5 = 0 has exactly one real root. Problem 46RE: Suppose that f is continuous on [0, 4], f(0) = 1, and 2 f(x) 5 for all x in (0, 4). Show that 9 ... Problem 47RE: By applying the Mean Value Theorem to the function f(x) = xl/5 on the interval [32, 33], show that... Problem 48RE: For what values of the constants a and b is (1,3) a point of inflection of the curve y = ax3 + bx2? Problem 49RE Problem 50RE: Find two positive integers such that the sum of the first number and four times the second number is... Problem 51RE: Show that the shortest distance from the point (x1, y1) to the straight line Ax + By + C = 0 is... Problem 52RE: Find the point on the hyperbola xy = 8 that is closest to the point (3, 0). Problem 53RE: Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of... Problem 54RE Problem 55RE Problem 56RE Problem 57RE: The velocity of a wave of length L in deep water is v=KLC+CL where K and C are known positive... Problem 58RE: A metal storage tank with volume V is to be constructed in the shape of a right circular cylinder... Problem 59RE: A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket price... Problem 60RE: A manufacturer determines that the cost of making x units of a commodity is... Problem 61RE Problem 62RE Problem 63RE Problem 64RE Problem 65RE Problem 66RE Problem 67RE: Find the most general antiderivative of the function. f(t) = 2 sin t 3et Problem 68RE Problem 69RE: Find f. f(t) = 2t 3 sin t, f(0) = 5 Problem 70RE Problem 71RE Problem 72RE Problem 73RE Problem 74RE Problem 75RE Problem 76RE Problem 77RE: A canister is dropped from a helicopter 500 m above the ground. Its parachute does not open, but the... Problem 78RE: In an automobile race along a straight road, car A passed car B twice. Prove that at some time... Problem 79RE: A rectangular beam will be cut from a cylindrical log of radius 10 inches. (a) Show that the beam of... Problem 80RE: If a projectile is fired with an initial velocity v at an angle of inclination from the horizontal,... Problem 81RE: If an electrostatic field E acts on a liquid or a gaseous polar dielectric, the net dipole moment P... Problem 82RE: If a metal ball with mass m is projected in water and the force of resistance is proportional to the... Problem 83RE Problem 84RE Problem 85RE Problem 86RE: Water is flowing at a constant rate into a spherical tank. Let V(t) be the volume of water in the... Problem 1P Problem 2P Problem 3P Problem 4P Problem 5P: Show that the inflection points of the curve y = (sin x)/x lie on the curve y2(x4 + 4) = 4. Problem 6P: Find the point on the parabola y = 1 x2 at which the tangent line cuts from the first quadrant the... Problem 7P: If a, b, c, and d are constants such that limxax2+sinbx+sincx+sindx3x2+5x4+7x6=8 find the value of... Problem 8P Problem 9P: Find the highest and lowest points on the curve x2 + xy + y2 = 12. Problem 10P Problem 11P: If P(a, a2) is any point on the parabola y = x2, except for the origin, let Q be the point where the... Problem 12P: For what values of c does the curve y = cx3 + ex have inflection points? Problem 13P: An isosceles triangle is circumscribed about the unit circle so that the equal sides meet at the... Problem 14P Problem 15P: The line y = mx + b intersects the parabola y = x2 in points A and B. (See the figure.) Find the... Problem 16P: ABCD is a square piece of paper with sides of length 1 m. A quarter-circle is drawn from B to D with... Problem 17P: For which positive numbers a does the curve y = ax intersect the line y = x? Problem 18P Problem 19P: Let f(x) = a1 sin x + a2 sin 2x + + an, sin nx, where a1, a2, , an are real numbers and n is a... Problem 20P: An arc PQ of a circle subtends a central angle as in the figure. Let A() be the area between the... Problem 21P: The speeds of sound c1 in an upper layer and c2 in a lower layer of rock and the thickness h of the... Problem 22P: For what values of c is there a straight line that intersects the curve y=x4+cx3+12x25x+2 in four... Problem 23P: One of the problems posed by the Marquis de IHospital in his calculus textbook Analyse des... Problem 25P Problem 26P: A hemispherical bubble is placed on a spherical bubble of radius 1. A smaller hemispherical bubble... format_list_bulleted
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning