Skip to main content

Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Single Variable Calculus: Early Transcendentals

Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it. Example 1 FIGURE 1 FIGURE 2 Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it. Example 1 FIGURE 1 FIGURE 2 6E Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it. Example 1 FIGURE 1 FIGURE 2 Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it. Example 1 FIGURE 1 FIGURE 2 Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it. Example 1 FIGURE 1 FIGURE 2 Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it. Example 1 FIGURE 1 FIGURE 2 11E 12E 13E 14E The graph shows how the average age of first marriage of Japanese men varied in the last half of the 20th century. Sketch the graph of the derivative function M'(t). During which years was the derivative negative?16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E Water temperature affects the growth rate of brook trout. The table shows the amount of weight gained by brook trout after 24 days in various water temperatures. Temperature(C) 15.5 17.7 20.0 22.4 24.4 Weight gained (g) 37.2 31.0 19.8 9.7 -9.8 If W(x) is the weight gain at temperature x, construct a table of estimated values for W' and sketch its graph. What are the units for W'(x)?Let P represent the percentage of a city's electrical power that is produced by solar panels t years after January 1, 2000. (a) What does dP/dt represent in this context? (b) Interpret the statement dpdt|t=2=3.5 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E 58E 59E Where is the greatest integer function f(x) = [[ x ]] not differentiable? Find a formula for[' and sketch its graph.61E (a) Sketch the graph of the function g(x) = x + |x|. (b) For what values of x is g differentiable? (c) Find a formula for g'63E 64E 65E 66E 67E State each differentiation rule both in symbols and in words. (a) The Power Rule (b) The Constant Multiple Rule (c) The Sum Rule (d) The Difference Rule (e) The Product Rule (f) The Quotient Rule (g) The Chain Rule 2RCC 3RCC 4RCC Give several examples of how the derivative can be interpreted as a rate of change in physics, chemistry, biology, economics, or other sciences.6RCC 7RCC 1RQ 2RQ 3RQ 4RQ 5RQ 6RQ Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. ddx(10x)=x10x1 8RQ 9RQ 10RQ 11RQ 12RQ 13RQ 14RQ Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If g(x) = x5, then g(x)=x5,thenlimx2g(x)g(2)x2=80 1RE 2RE 3RE 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE Calculate y'. 12. y = (arcsin 2x)2 13RE 14RE 15RE 16RE Calculate y'. 17. y=arctan 18RE 19RE 20RE 21RE 22RE 23RE 24RE 25RE 26RE 27RE 28RE 29RE Calculate y'. 30. y=(x2+1)4(2x+1)3(3x1)5 31RE 32RE 33RE 34RE 35RE 36RE 37RE 38RE 39RE 40RE 41RE 42RE 43RE 44RE 45RE 46RE 47RE 48RE 49RE 50RE 51RE 52RE 53RE 54RE 55RE 56RE 57RE 58RE 59RE 60RE 61RE 62RE 63RE 64RE 65RE 66RE 67RE 68RE 69RE 70RE 71RE 72RE 73RE 74RE 75RE 76RE 77RE 78RE 79RE 80RE 81RE 82RE 83RE 84RE 85RE 86RE 87RE A particle moves along a horizontal line so that its coordinate at time t is x=b2+c2t2,t0 where b and c are positive constants. (a) Find the velocity and acceleration functions. (b) Show that the particle always moves in the positive direction.A particle moves on a vertical line so that its coordinate at time t is y = t3 12t + 3, t 0. (a) Find the velocity and acceleration functions. (b) When is the particle moving upward and when is it moving downward? (c) Find the distance that the particle travels in the time interval 0 1 3. (d) Graph the position, velocity, and acceleration functions for 0 t. 3. (e) When is the particle speeding up? When is it slowing down?90RE 91RE 92RE 93RE 94RE 95RE 96RE 97RE 98RE A balloon is rising at a constant speed of 5 ft/s. A boy is cycling along a straight road at a speed of 15 ft/s. When he passes under the balloon, it is 45 ft above him. How fast is the distance between the boy and the balloon increasing 3 s later?100RE 101RE 102RE 103RE 104RE 105RE 106RE 107RE 108RE 109RE Suppose f is a differentiable function such that f(g(x)) = x and f(x) = 1 + [f(x)]2. Show that g(x) = 1/(1 + x2).111RE 112RE 1P 2P 3P 4P 5P 6P 7P 8P 9P 10P 11P 12P 13P If f(x)=x46+x45+21+x, calculate f(46)(3). Express your answer using factorial notation: n! = 123(n 1) n.The figure shows a rotating wheel with radius 40 cm and a connecting rod AP with length 1.2 m. The pin P slides back and forth along the x-axis as the wheel rotates counterclockwise at a rate of 360 revolutions per minute. (a) Find the angular velocity of the connecting rod. d/ dt, in radians per second, when = /3. (b) Express the distance x = | OP | in tenus of . (c) Find an expression for the velocity of the pin P in terms of .16P 17P 18P Let T and N be the tangent and normal lines to the ellipse x2/9 + y2/4 = 1 at any point P on the ellipse in the first quadrant. Let xT and yT be the x- and y-intercepts of T and xN and yN be the intercepts of N. As P moves along the ellipse in the first quadrant (but not on the axes), what values can .:xT, yT, xN, and yN take on? First try to guess the answers just by looking at the figure. Then use calculus to solve the problem and see how good your intuition is.20P 21P Let P(x1, y1) be a point on the parabola y2 = 4px with focus F(p, 0). Let be the angle between the parabola and the line segment FP, and let be the angle between the horizontal line y = y1, and the parabola as in the figure. Prove that = . (Thus. by a principle of geometrical optics. light from a source placed at F will be reflected along a line parallel to the x-axis. This explains why paraboloids, the surfaces obtained by rotating parabolas about their axes, are used as the shape of some automobile headlights and mirrors for telescopes.)23P 24P 25P 26P 27P 28P 29P 30P Find the two points on the curve y = x4 2x2 x that have a common tangent line.32P 33P 34P 35P (a) How is the number e defined? (b) Use a calculator to estimate the values of the limits limh02.7h1handlimh02.8h1h correct to two decimal places. What can you conclude about the value of e?2E Differentiate the function. f(x) = 240 Differentiate the function. f(x) = e5 Differentiate the function. f(x) = 5.2x + 2.3 6E 7E Differentiate the function. f(t) = 1.4t5 2.5t2+ 6.7 9E 10E 11E Differentiate the function. B(y) = cy6 13E Differentiate the function. y = x5/3 x2/3 Differentiate the function. R(a) = (3a + 1)2 Differentiate the function. h(t)=t44et Differentiate the function. S(p)=pp Differentiate the function. y=x3(2+x)Differentiate the function. y=3ex+4x3 Differentiate the function. S(R) = 4R2 21E 22E 23E 24E 25E 26E 27E 28E 29E Differentiate the function. D(t)=1+16t2(4t)3 31E Differentiate the function. y = ex + 1 + 1 33E Find an equation of the tangent line to the curve at the given point. y = 2ex + x, (0, 2)Find an equation of the tangent line to the curve at the given point. y=x+2x,(2,3)36E Find equations of the tangent line and normal line to the curve at the given point. y = x4 + 2ex, (0, 2)38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E Find the points on the curve y = 2x3 + 3x2 12x + 1 where the tangent is horizontal.56E 57E 58E 59E 60E 61E Where does the normal line to the parabola y = x2 1 at the point (1, 0) intersect the parabola a second time? Illustrate with a sketch.Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, 4). Find the coordinates of the points where these tangent lines intersect the parabola.64E 65E Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs. (a) f(x) = xn (b) f(x) = 1/x 67E

Page: [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]