Solutions Modeling Dynamics of Life 3ed Adler - Chapter 2.4

2.4.1 Expand the following binomials. ...
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2.4.2 Expand the following binomials. ...
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2.4.3 Expand the following binomials. ...
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2.4.4 Expand the following binomials. ...
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2.4.5 On the following graphs, identify points where
a. the function is not continuous,
b. the function is not differentiable (and say why),
c. the derivative is zero (critical points). ...
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2.4.6 On the following graphs, identify points where
a. the function is not continuous,
b. the function is not differentiable (and say why),
c. the derivative is zero (critical points). ...
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2.4.7 Find the derivatives of the following functions. Write your answers in both differential and prime notation. Which functions are increasing and which are decreasing? M ( x )=0.5x + 2.
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2.4.8 Find the derivatives of the following functions. Write your answers in both differential and prime notation. Which functions are increasing and which are decreasing? L ( t )=2t + 30.
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2.4.9 Find the derivatives of the following functions. Write your answers in both differential and prime notation. Which functions are increasing and which are decreasing? g ( y )=−3y + 5.
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2.4.10 Find the derivatives of the following functions. Write your answers in both differential and prime notation. Which functions are increasing and which are decreasing? Q ( z )=−3.5×...
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2.4.11 For each of the following quadratic functions, find the slope of the secant line connecting x = 1 and x = 1 + Δx, and the slope of the tangent line at x =1 by taking the limit. ...
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2.4.12 For each of the following quadratic functions, find the slope of the secant line connecting x = 1 and x = 1 + Δx, and the slope of the tangent line at x =1 by taking the limit. ...
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2.4.13 For each of the following quadratic functions, find the slope of the secant line connecting x and x + Δx, and the slope of the tangent line as a function of x. Write your result in both differential and prime notation. ... Reference Exercise 11 ...
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2.4.14 For each of the following quadratic functions, find the slope of the secant line connecting x and x + Δx, and the slope of the tangent line as a function of x. Write your result in both differential and prime notation. ... Reference Exercise 12 ...
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2.4.15 For each of the following quadratic functions, graph the function and the derivative. Identify critical points, points where the function is increasing, and points where the function is decreasing. ... (based on Exercise 13). reference Exercise 13 ...
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2.4.16 For each of the following quadratic functions, graph the function and the derivative. Identify critical points, points where the function is increasing, and points where the function is decreasing. ... (based on Exercise 14). reference Exercise 13 ...
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2.4.17 On the figures, label the following points and sketch the derivative.
a. One point where the derivative is positive.
b. One point where the derivative is negative.
c. The point with maximum derivative.
d. The point with minimum (most negative) derivative.
e. Points with derivative of zero (critical points). ...
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2.4.18 On the figures, label the following points and sketch the derivative.
a. One point where the derivative is positive.
b. One point where the derivative is negative.
c. The point with maximum derivative.
d. The point with minimum (most negative) derivative.
e. Points with derivative of zero (critical points). ...
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2.4.19 On the figures, identify which of the curves is a graph of the derivative of the other. ...
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2.4.20 On the figures, identify which of the curves is a graph of the derivative of the other. ...
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2.4.21 On the figures, identify which of the curves is a graph of the derivative of the other. ...
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2.4.22 On the figures, identify which of the curves is a graph of the derivative of the other. ...
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2.4.23 The following functions all fail to be differentiable at x = 0. In each case, graph the function, see what happens if you try to compute the derivative as the limit of the slopes of secant lines, and say something about the tangent line. The absolute value function f (x) = |x|.
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2.4.24 The following functions all fail to be differentiable at x = 0. In each case, graph the function, see what happens if you try to compute the derivative as the limit of the slopes of secant lines, and say something about the tangent line. The square root function ... (Because this function is only defined for x ≥ 0, you can only use Δx > 0.)
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2.4.25 The following functions all fail to be differentiable at x = 0. In each case, graph the function, see what happens if you try to compute the derivative as the limit of the slopes of secant lines, and say something about the tangent line. The Heaviside function (Section 2.3, Exercise 25), defined by ...
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2.4.26 The signum function defined by ...
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2.4.27 The following graphs show the temperature of different solutions with chemical reactions as functions of time. Graph the rate of change of temperature in each case, and indicate when the solution is warming up and when it is cooling down. ...
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2.4.28 The following graphs show the temperature of different solutions with chemical reactions as functions of time. Graph the rate of change of temperature in each case, and indicate when the solution is warming up and when it is cooling down. ...
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2.4.29 The following graphs show the temperature of different solutions with chemical reactions as functions of time. Graph the rate of change of temperature in each case, and indicate when the solution is warming up and when it is cooling down. ...
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2.4.30 A bear sets off in pursuit of a hiker. Graph the position of a bear and hiker as functions of time from the following descriptions. Both move at constant speed, but the bear is faster and eventually catches the hiker.
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2.4.31 A bear sets off in pursuit of a hiker. Graph the position of a bear and hiker as functions of time from the following descriptions. Both increase speed until the bear catches the hiker.
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2.4.32 A bear sets off in pursuit of a hiker. Graph the position of a bear and hiker as functions of time from the following descriptions. Both increase speed until the bear catches the hiker.
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2.4.33 A bear sets off in pursuit of a hiker. Graph the position of a bear and hiker as functions of time from the following descriptions. The bear increases speed and the hiker steadily slows down until the bear catches the hiker.
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2.4.34 A bear sets off in pursuit of a hiker. Graph the position of a bear and hiker as functions of time from the following descriptions. The bear runs at constant speed, the hiker steadily runs faster until the bear gives up and stops. The hiker slows down and stops soon after that.
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2.4.35 An object dropped from a height of 100 m has distance above the ground of ... where a is the acceleration of gravity. For each of the following planets with the given acceleration, find the time when the object hits the ground, and the speed of the object at that time. On Earth, where a = 9.78 ....
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2.4.36 An object dropped from a height of 100 m has distance above the ground of ... where a is the acceleration of gravity. For each of the following planets with the given acceleration, find the time when the object hits the ground, and the speed of the object at that time. On the moon, where a = 1.62 ....
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2.4.37 An object dropped from a height of 100 m has distance above the ground of ... where a is the acceleration of gravity. For each of the following planets with the given acceleration, find the time when the object hits the ground, and the speed of the object at that time. On Jupiter, where a = 22.88 ....
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2.4.38 An object dropped from a height of 100 m has distance above the ground of ... where a is the acceleration of gravity. For each of the following planets with the given acceleration, find the time when the object hits the ground, and the speed of the object at that time. On Mars’ moon Deimos, where ...
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2.4.39 Have your computer plot the following for the function ... Use base point t = 1.
a. The secant line with Δt = 1.
b. The secant line with Δt =−1.
c. The secant line with Δt = 0.1.
d. The secant line with Δt =−0.1.
e. Use smaller and smaller values of Δt and try to estimate the slope of the tangent. Graph it, then zoom in on your graph. Does the tangent look right?
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