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All Textbook Solutions for Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False: x2 + 6x + 2y = 1 defines y as a function of x.2PT The implied domain of is: (1, ∞) (−∞, 1) x ≠ 1 (−1, 1) 4PT 5PT 6PT 1PT 2PT 3PT 4PT 1PT 2PT 3PT 4PT 5PT 6PT 7PT 1PT A mosquito population of 100 grows to 500 after two weeks. If the population follows an exponential growth model, how many mosquitoes are there after 5 weeks? a) 1069 b) 1100 c) 5590 d) 31250 3PT 4PT A function f is one-to-one means: if x1 = x2, then f(x1) = f(x2) if x1 ≠ x2, then f(x1) = f(x2) if x1 ≠ x2, then f(x1) = f (x2) if f(x1) ≠ f(x2), then x1 ≠ x2 2PT 3PT 4PT 5PT True or False: ln(a + b) = ln a + ln b. 7PT 8PT 9PT 1PT 2PT 3PT True or False: The slope of a tangent line may be interpreted as average velocity. 1PT 2PT 3PT 4PT 5PT 6PT True or False: The graph in question 3 has a vertical asymptote at x = 1.1PT 2PT 3PT 4PT 5PT 6PT 7PT 1PT 2PT 3PT 4PT Sometimes, Always, or Never: If limxaf(x) and f(a) both exist, then f is continuous at a.2PT 3PT 4PT 5PT 6PT 1PT 2PT 3PT 4PT 5PT 6PT 7PT 8PT 9PT 1PT The slope of the tangent line to y = x3 at x = 2 is: 18 12 6 0 3PT 4PT 5PT 6PT 7PT 8PT 9PT Which is the largest? a) f(a) b) f(b) c) f(c) d) cannot tell from information given True or False: f(x) = tan x is differentiable at x=2.2PT 3PT 4PT 1PT 2PT 3PT 4PT 5PT 6PT 1PT 2PT 3PT 4PT 1PT 2PT 3PT 4PT 5PT 6PT 1PT 2PT 3PT 4PT 5PT 6PT 7PT 1PT 2PT 3PT 4PT 5PT 6PT 1PT 2PT 3PT 4PT 5PT 1PT 2PT 3PT 4PT 1PT A bacteria culture starts with 50 organisms and after 2 hours there are 100. Assuming natural growth, how many will there be after 5 hours? a) 50 ln 5 b) 50e5 c) 2002 d) 300 3PT A right triangle has one leg with constant length 8 cm. The length of the other leg is decreasing at 3 cm/sec. The rate of change of the hypotenuse when the variable leg is 6 cm is: a) 95cm/s b) 3 cm/s c) 53cm/s d) 53cm/s 2PT 1PT 2PT 3PT 4PT 1PT 2PT 3PT 4PT 5PT 1PT Sometimes, Always, or Never: If f(c) = 0, then c is a critical number.The critical numbers of f(x) = 3x4 = 20x3 36x2 are: a) 0, 1, 6 b) 0, 1, 6 c) 0, 1, 6 d) 0, 1, 6 4PT True or False: The absolute extrema of a continuous function on a closed interval always exist.6PT 7PT 1PT 2PT 3PT True or False: If f(x) = g(x) for all x then f(x) = g(x).5PT 1PT 2PT 3PT 4PT 5PT 6PT True or False: If f(c) = 0, then c is a point of inflection for f.8PT 9PT 10PT 1PT 2PT 3PT limx(lnx)1/x= a) 0 b) 1 c) e d)1PT 2PT 3PT True or False: If f(x) 0 for all x in an interval I then f is increasing on I.5PT 6PT 7PT 1PT 2PT 3PT 1PT A carpenter has a 10-foot-long board to mark off a triangular area on the floor in the corner of a room. See the figure. What is the function for the triangular area in terms of x that may be used to determine the maximum such area? a) A=12x2 b) A=12(x2+10) c) A=12x100x2 d) A=12x1002x2 3PT 4PT 1PT 2PT 3PT 1PT 2PT 3PT 4PT 5PT 1PT 2PT 3PT If the interval [1, 3] is divided into n subintervals of length x, then the shaded area at the right is a) limni=1n((xi)2+1))x b) limni=1n((31)2+1)x c) limni=1n(3(xi)2+xi)x d) limni=1n((xi)33+xi)x 1PT 2PT 3PT 4PT 5PT 6PT 7PT 8PT 9PT 1PT 2PT 3PT 4PT 1PT 2PT 3PT 4PT 5PT 6PT 1PT 2PT 3PT 4PT 5PT 6PT 7PT 1PT 2PT A definite integral for the area of the region bounded by y = 2 − x2 and y = x2 is: Find a definite integral for the volume of a solid with a circular base of radius 4 inches such that the cross section of any slice perpendicular to a certain diameter in the base is a square. 2PT 3PT 1PT 2PT 1PT A particle moves along an x-axis from 2 m to 3 m pushed by a force of x2 N (newtons) for 2 ≤ x ≤ 3. The definite integral that determines the amount of work done is: A circular tank with radius 1 m and height 2 m is filled with a liquid whose density is 250 kg/m3. Find a definite integral for the work done pumping all the liquid over the top edge. a) 01(250)(9.8)(2)xdx b) 01(250)(9.8)()xdx c) 02(250)(9.8)(2)xdx d) 02(250)(9.8)()xdx 1PT 2PT 3PT 4PT 1PT 2PT 3PT The integration by parts rule corresponds to which differentiation formula? (u + v)′ = u′ + v′ (uv)′ = u′v′ (uv)′ = uv′ + u′v u dv = v du By the methods of trigonometric integrals, sin3 x cos2 x dx should be rewritten as: a) sin3 x (1 sin2 x)dx b) (1 cos2 x)3/2 cos2 x dx c) (sin3 x)(cos x) cos x dx d) (1 cos2 x) cos2 x sin x dx 2PT The first step to evaluate cos4 x dx is to rewrite the integral as a) (1+cos2x2)2dx b) cos3xcosxdx c) (1sin4x)dx d) cos2x(1sin2x)dx ∫ sin 3x cos 6x dx = 1PT 2PT 3PT 4PT 1PT 2PT 3PT 4PT 5PT 1PT 2PT 3PT 4PT 5PT 6PT 1PT 2PT 3PT 4PT 1PT 2PT 3PT 4PT True or False: 23xdx is an improper integral.2PT 3PT 4PT A definite integral for the length of y = x3, 1 x 2 is a) 121+x3dx b) 121+x6dx c) 121+9x4dx d) 121+3x2dx 2PT 3PT 1PT A hollow cylinder with no ends of radius 3 cm and height 4 cm is a surface of revolution. Its surface area may be expressed as: a) 032(4)1+0dx b) 032(3)1+0dx c) 042(3)1+0dx d) 042(4)1+0dx 1PT 2PT The y-coordinate of the center of mass of the region bounded by , x = 1, x = 5, y = 0 is: 4 The lamina at the right has center of mass (38,65) and uniform density . The moments about the x- and y-axes are, respectively, and . a) 512 and 43 b) 43 and 512 c) 125 and 34 d) 34 and 125 True or False: In many applications of definite integrals, the integral is used to compute the total amount of a varying quantity.2PT 3PT 1PT 2PT 3PT 4PT 1PT 2PT 3PT 4PT 1PT 2PT 3PT 1PT True or False: y′ + xey = ex+y is separable. 3PT 4PT 1PT 2PT 3PT 4PT 1PT 2PT 3PT 1PT 2PT 3PT 1PT 2PT

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