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Instituto Polit´ cnico Nacional e Rafael Cervantes

Unidad Profesional Interdsciplinaria de Ingenier´a Campus Guanajuato ı C´ lculo Diferencial e Integral a

Tarea3. Fecha de Entrega: 09/04/2010 at 10:00pm CDT. 4. (1 pt)

1. (1 pt) Use interval notation to indicate the domain of f (x) = and g(x) =
7 4

x2 − 5x

11x2 − 8x.

The domain of f (x) is The domain of g(x) is 2. (1 pt)Give the domain and range (to the nearest half integer) of the function illustrated above. Domain: [ , ] Range: [ , ]

3. (1 pt) For small changes in temperature, the formula for the expansion of a metal rod under a change in temperature is: g − L = aL(t − T ), where g is the length of the object at temperature t , and L is the length at temperature T , and a is a constant which depends on the typeof metal. 1. Express g as a linear function of t . Find the slope and vertical intercept in terms of L , T , and a. slope = intercept = 2. A rod is 195 cm long at 85 degrees F and made of a metal with a = 10−4 . Write an equation giving the length of this rod at temperature t (because a = 10−4 is very small, give an exact answer: do not round expand multiplied numerical products to get roundeddecimals). cm g= (What does the sign of the slope tell you about the expansion of a metal under a change in temperature?)
1

The graph above illustrates your north-south distance in miles from the edge of a lake in hours from noon (where positive values mean you are north of the lake). When the graph passes through the axis, it means you pass by the edge of the lake (so your distance is 0).Complete the following description of your journey, selecting the correct descriptions of directions and filling in the numerical values for the indicated distances and speeds. miles from the lake relaxing. ”At noon I am a distance of I then jump on my bike and start to cycle ? the lake at a speed of mph. At 3pm I stop for a rest and a picnic for three hours. I then jump back on my bike and cycle ? thelake at a speed of mph. At 8pm I arrive at my house which is a distance of miles from the lake.” 5. (1 pt) Let x+2 f (x) = 2 . x + 6x − 16 Use interval notation to indicate the domain of f (x). Note: When entering interval notation in WeBWorK, use I for ∞, -I for −∞, and U for the union symbol. If the set is empty, enter empty . Domain = 6. (1 pt) Suppose that a rectangle has a perimeter of 25meters. Express the area A(x) of the rectangle in terms of the length x of one of its sides. A(x) = 7. (1 pt) Find an expression for the function f (x) whose graph is a line passing through the points (5, −5) and (3, −9). f (x) = 8. (1 pt) For each of the following functions, decide whether it is even, odd, or neither. Enter E for an EVEN function, O for an ODD function and N for a function which isNEITHER even nor odd.

1. 2. 3. 4.

f (x) = x6 − 6x8 + 3x2 f (x) = x6 + 3x8 + 2x−5 f (x) = x1 + x9 + x−5 f (x) = −5x6 − 3x8 − 2

9. (1 pt)

x= y= (b) y = 3 f (x) x= y= (c) y = f (x + 4) x= y= (d) y = 2 − f (x) x= y=

-4

-2

0

2

4

-4

-2

0

2

4

-4

-2

0

2

4

-4

-2

0

2

4

Note: Click on graph for larger version in new browser window.The above graph is the plot of the piecewise-defined function   f1 (x) x < 0  f (x) = f2 (x) 0 ≤ x ≤ 3   f3 (x) x > 3 Find formulas for f1 (x), f2 (x), and f3 (x). f1 (x) = f2 (x) = f3 (x) = 10. (1 pt) Find an expression for the function f (x) whose graph is given by the bottom half of the parabola x + (y − 3)2 = 0. f (x) = 11. (1 pt) Consider the function f (x) given by

12. (1 pt)Poiseuille’s Law gives the rate of flow, R, of a gas through a cylindrical pipe in terms of the radius of the pipe, r, for a fixed drop in pressure between the two ends of the pipe. (a) Find a formula for Poiseuille’s Law, given that the rate of flow is proportional to the fourth power of the radius. R= (Use k for any constant of proportionality you may have in your equation.) (b) If R = 500 cm3 /s in a...
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