Rewrite the expression without using the absolute value symbol. |x – 2| if x < 2
> Show that the points (-2, 9), (4, 6), (1, 0), and (-5, 3) are the vertices of a square.
> Find an equation of the perpendicular bisector of the line segment joining the points A (1, 4) and B (7, -2).
> Find the midpoint of the line segment joining the points (1, 3) and (7, 15).
> Show that the midpoint of the line segment from P1 (x1, y1) to P2 (x2, y2) is (x1 + x2/2, y1 + y2/2).
> Show that the lines 3x – 5y + 19 = 0 and 10x + 6y – 50 = 0 are perpendicular and find their point of intersection.
> Show that the lines 2x – y = 4 and 6x – 2y = 10 are not parallel and find their point of intersection.
> Show that the equation represents a circle and find the center and radius. x² + y² + 6y + 2 = 0
> Find the slope of the line through P and Q. P (-1, -4), Q (6, 0)
> Show that the equation represents a circle and find the center and radius. x? + y? – 4x + 10y + 13 = 0
> Find the area of the region that lies inside both curves. r = 3 + 2 cos e, r= 3 + 2 sin e
> Find an equation of a circle that satisfies the given conditions. Center (-1, 5), passes through (-4, -6)
> Find an equation of a circle that satisfies the given conditions. Center (3, -1), radius 5
> Sketch the region in the xy-plane. {(x, y) | -x < y < 1/2 (x + 3)}
> Sketch the region in the xy-plane. {(x, y) |1 + x < y < 1 – 2x}
> Sketch the region in the xy-plane. {(x, y) | y > 2x – 1}
> Sketch the region in the xy-plane. {(x, y) |0 < y < 4 and x < 2}
> Sketch the region in the xy-plane. {(x. y) ||x| < 3 and |y| < 2}
> Sketch the region in the xy-plane. {(x, y) ||x| < 2
> Sketch the region in the xy-plane. {(x, y) | x > 1 and y < 3}
> Find the slope of the line through P and Q. P (-3, 3), Q (-1, -6)
> (a). Use a graph to guess the value of the limit (b). Use a graph of the sequence in part (a) to find the smallest values of N that correspond to ∈ = 0.1 and ∈ = 0.001 in Definition 3. lim - n!
> Sketch the region in the xy-plane. {(x, y) |x < 0}
> Find the slope and -intercept of the line and draw its graph. 4x + 5y = 10
> Find the slope and -intercept of the line and draw its graph. 3x – 4y = 12
> Find the slope and -intercept of the line and draw its graph. 2x – 3y + 6 = 0
> Find the slope and -intercept of the line and draw its graph. x + 3y = 0
> Find an equation of the line that satisfies the given conditions. Through (1/2, -2/3), perpendicular to the line 4x – 8y = 1
> Find an equation of the line that satisfies the given conditions. Through (-1, -2), perpendicular to the line 2x + 5y + 8 = 0
> Find an equation of the line that satisfies the given conditions. y-intercept 6, parallel to the line 2x + 3y + 4 = 0
> Find an equation of the line that satisfies the given conditions. Through (1, -6), parallel to the line x + 2y = 6
> Find an equation of the line that satisfies the given conditions. Through (4, 5), parallel to the -axis
> (a). For what values of x is it true that 1/x2 > 1,000,000 (b). The precise definition of limx→a f (x) = ∞ states that for every positive number M (no matter how large) there is a corresponding positive number δ such that if 0 < |x – a| < δ, then f (x) >
> Find the distance between the points. (1, -3) (5, 7)
> Find an equation of the line that satisfies the given conditions. Through (4, 5), parallel to the -axis
> Find an equation of the line that satisfies the given conditions. x-intercept -8, y-intercept 6
> Find an equation of the line that satisfies the given conditions. x-intercept, y-intercept -3
> Find an equation of the line that satisfies the given conditions. Slope 2/5, y-intercept 4
> Find an equation of the line that satisfies the given conditions. slope 3, y-intercept -2
> Find an equation of the line that satisfies the given conditions. Through (-1, -2), and (4, 4)
> Find an equation of the line that satisfies the given conditions. Through (2, 1), and (1, 6)
> Find an equation of the line that satisfies the given conditions. Through (-3, -5), slope -7/2
> Find an equation of the line that satisfies the given conditions. Through (2, -3), slope 6
> For the limit illustrate Definition 2 by finding values of N that correspond to ∈ = 0.5 and ∈ = 0.1. 4x2 + 1 lim = 2 x + 1
> Sketch the graph of the equation. |y| = 1
> Find the distance between the points. (1, 1), (4, 5)
> Rewrite the expression without using the absolute value symbol. |x2 + 1|
> Rewrite the expression without using the absolute value symbol. |2x – 1|
> Rewrite the expression without using the absolute value symbol. |x + 1|
> Rewrite the expression without using the absolute value symbol. |x – 2| if x > 2
> Show that if 0 < a < b, then a2 < b2.
> Prove that |ab| = |a||b|. [Hint: Use Equation 3.]
> Solve the inequality ax + b + c for x, assuming that a, b, and are negative constants.
> Use a graph to find a number N such that if x > N then |6х? + 5х — 3 3 < 0.2 2x2 – 1
> Solve the inequality a (bx – c) > bc for x, assuming that a, b, and are positive constants.
> Solve the inequality. |5x – 2| < 6
> Rewrite the expression without using the absolute value symbol. ||-2| - |-3||
> Solve the inequality. |2x – 3| < 0.4
> Solve the inequality. |x + 1|> 3
> Solve the inequality. |x + 5| > 2
> Solve the inequality. |x – 6| < 0.1
> Solve the inequality. |x – 4| < 1
> Solve the inequality. |x| > 3
> Solve the inequality. |x| < 3
> (a). How would you formulate an ∈1δ definition of the one-sided limit limx→a+ f (x) = L? (b). Use your definition in part (a) to prove that limx→a+ √x = 0.
> Solve the equation for x. |3x + 5| = 1
> Solve the equation for x. |x + 3| = |2x + 1|
> Rewrite the expression without using the absolute value symbol. |√5 – 5|
> Use the relationship between C and F given in Exercise 27 to find the interval on the Fahrenheit scale corresponding to the temperature range 20 < C < 30. Exercise 27: The relationship between the Celsius and Fahrenheit temperature scales is given by C
> The relationship between the Celsius and Fahrenheit temperature scales is given by C = 5/9 (F – 32), where C is the temperature in degrees Celsius and is the temperature in degrees Fahrenheit. What interval on the Celsius scale corresponds to the tempera
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. 1/x < 4
> (a). Use Exercise 69 to show that the angle between the tangent line and the radial line is ψ = Ï€/4 at every point on the curve r = eθ. Exercise 69: Let P be any point (except the origin) on the curve r = f (Î&c
> Let P be any point (except the origin) on the curve r = f (θ). If ψ is the angle between the tangent line at P and the radial line OP, show that [Hint: Observe that ψ = φ - θ in the figure.]
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. (x + 1)(x – 2)(x + 3) > 0
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. x³ – x? < 0
> Identify the curve by finding a Cartesian equation for the curve. r= 3 sin e
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. x2 > 5
> Rewrite the expression without using the absolute value symbol. |π - 2|
> Use a graph to estimate the -coordinate of the highest points on the curve r = sin 2θ. Then use calculus to find the exact value.
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. x? < 2x + 8 2.1
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. (x – 1)(x – 2) > 0
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. 1< 3x + 4 < 16
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. 0 <1- x<1
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. 1+ 5x > 5 – 3x
> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. 1 — х<2
> Show that the polar equation r = a sin θ + b cos θ, where ab ≠ 0, represents a circle, and find its center and radius.
> A crystal growth furnace is used in research to determine how best to manufacture crystals used in electronic components for the space shuttle. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power.
> In this project we give a unified treatment of all three types of conic sections in terms of a focus and directrix. We will see that if we place the focus at the origin, then a conic section has a simple polar equation. In Chapter 10 we will use the pola
> An anticodon has the sequence GCG. What amino acid does this tRNA carry? What would be the effect of a mutation that changed the C of the anticodon to a G?
> Most of the carbon dioxide used in photosynthesis comes from _______. a. glucose b. the atmosphere c. rainwater d. photolysis
> A C3 plant absorbs a carbon radioisotope (as part of 14CO2). In which compound does the labeled carbon appear first? Which compound forms first if a C4 plant absorbs the same radioisotope?
> 1. Photosynthesis runs on the energy of ______. a. light b. hydrogen ions c. O2 d. CO2 2. In cyanobacteria and photosynthetic eukaryotes, the light-dependent reactions proceed in/at the ______. a. thylakoid membrane b. plasma membrane c. stroma d. cytop
> While gazing into an aquarium, you see bubbles coming from an aquatic plant (right). What are the bubbles?
> A cat eats a bird, which ate a caterpillar that chewed on a weed. Which organisms are autotrophs? Which ones are heterotrophs?
> _______ cannot easily diffuse across a lipid bilayer. a. Water b. Gases c. Ions d. all of the above
> All antioxidants ______. a. prevent other molecules from being oxidized b. are coenzymes c. balance charge d. deoxidize free radicals
> A molecule that donates electrons becomes ______, and the one that accepts electrons becomes ______. a. reduced; oxidized b. ionic; electrified c. oxidized; reduced d. electrified; ionic
> Immerse a human red blood cell in a hypotonic solution, and water _______. a. diffuses into the cell b. diffuses out of the cell c. shows no net movement d. moves in by endocytosis
> What accumulates inside the thylakoid compartment of chloroplasts during the light-dependent reactions? a. glucose b. hydrogen ions c. O2 d. CO2
> On the geologic time scale, life originated in the _______. a. Archaean b. Proterozoic c. Phanerozoic d. Cambrian
> A chromosome contains many different gene regions that are transcribed into different __________. a. proteins b. polypeptides c. RNAs d. a and b
