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Answers seem to be approaching 7. First, consider the line through the points 0, 5 and 5, 0. Median Marriage Age for The first derivative is positive because the temperature is dropping. Thus, m is not defined and there is no y- m is not defined and there is no y-intercept. A function can have a corner or vertical a sudden jump, and so a steady rate of change tangent and still be continuous. The tangent line has zero error at the point and errors near the point that differ as little as possible from zero.

Sales are increasing by 38 million units per b. The sales at the end of is c.

Substitute 12 into the equation: First, find the slope of the line containing the First, find the slope of the line containing points. Substitute 20 into the equation.

Since is 12 years after , substitute 11 into the equation. Substitute each pair into the equation. Every pair gives 15, Median Marriage Age for The x-value corresponding to the year b. The x-value corresponding to the year c.

To find the probability that a person with b. The probability that a person with a c. Cigarette consumption is declining by b. Each year the usage increases by about 5.

The male life expectancy is increasing by b. The female life expectancy is increasing by 2. Future longevity decreases by 0. Seat belt use increases by 8. It would not make sense to use the d. Infinity is not a number. All negative numbers must be less than zero, and all positive numbers are more than zero.

Therefore, all negative numbers are less than all positive numbers. The slope of a vertical line is undefined. The slope of a vertical line is undefined, so a vertical line does not have a slope. It should be. Drawing a picture of a right triangle. To obtain the slope-intercept form of a equation and solve for x: Substitute 0 for b and solve for x: Average body thickness Given the unemployment rate of 2 percent, Given the unemployment rate of 5 percent, b.

Time to build the 50th Boeing Therefore, the land area must be increased by a factor of more than 18 to increased by almost times to triple the double the number of species.

For example, expression to be defined. Yes 2. Yes 5. Yes 7.

Yes 9. Thus, defined only for positive values of x.

The vertex is —20, The vertex is 40, — Their slopes are all 2, but they have a. The lines have the same y-intercept, but different y-intercepts. The line 2 units below the line of the b. Then To find the break-even points, set C x b.

To find the number of devices that equal to R x and solve the resulting maximizes profit, first find the profit equation. To find the number of bicycles that equal to R x and solve the resulting maximizes profit, first find the profit equation.

The maximum 6 6 profit is found by evaluating P To find the number of exercise machines equal to R x and solve the resulting that maximizes profit, first find the profit equation. Since this is a parabola that opens downward, On [10, 16] by [0, ]. The upper limit is b. A function can have more than one x-intercept. A that x increasing by 1 means y increases by 2. Because the function is linear and 5 is halfway If a is positive, then the prendles and y is in blargs.

No, that would violate the vertical line test. Either by the symmetry of parabolas, or, better, Note: A parabola is a geometric shape and so by taking the average of the two x-intercepts: Functions 7. Polynomial Piecewise linear function Rational function None of these Yes, 2.

The intersection point is 12, First find the composition R v t. We must find the composition R p t. Substitute 8 for x. That means, all So it should be drawn like. Yes b. Yes, because the composition of two polynomials involves raising integral powers to integral powers.

Since the vertical line passes through the First, calculate the slope from the two points. Now use the point-slope formula with this 2 slope and the point —1, 3.

To To find the find the slope, use the slope formula with the slope, use the slope formula with the points 0, points 0, —1 and 1, 1. Use the straight-line depreciation The number is increasing by about 3D screens per year. Yes No To find y, evaluate f —7.

To find the break even points, solve the To find the number of receivers that The installed per month. The maximum profit is maximum profit is found by evaluating found by evaluating P The advertising budget A as a function of t is Derivatives and Their Uses 41 Chapter 2: Derivatives and Their Uses Continuous Discontinuous at c because f c is not defined.

Discontinuous at c because lim f x does not exist. Continuous c. Discontinuous because lim f x does not exist. Thus, consider of x for which the denominator is zero. From Exercise 37, we know lim f x does not Therefore, the function is discontinuous exist. From Exercise 39, we know From Exercise 41, we know Therefore the function is discontinuous at x continuous. From the graph, we can see that lim f x does As x approaches c, the function is approaching In a continuous function, when x equals c, the lim f x even if the value of the function at c is function equals lim f x.

The value of the function at 2 has nothing Both one-sided limits would have to exist On the left side of the limit exists and Therefore one side of the equation is defined and the other is not. The third requirement for continuity at The jumps agree, so if one is 7 the other must be 7.

The slope is positive at P1. The slope is zero at P1. The slope is negative at P2. The slope is positive at P2.

The slope is zero at P3. The slope is negative at P3. The slope is negative at P1. The slope is zero at P2. The tangent line at P1 contains the points 0, 2 6.

The tangent line at P1 contains the points 1, 4 and 1, 5. The slope of this line is and 4, 3. The tangent line at P2 contains the points 3, 5 The tangent line at P2 contains the points 5, 3 and 5, 4.

The slope of this line is and 6, 5. The slope of the curve at P2 is 2. Your graph should look roughly like the 8. Your graph should look roughly like the following: Answers seem to be approaching 3. Answers seem to be approaching 4. Answers seen to be approaching 9. Answers seem to be approaching 6.

Answers seem to be approaching 5. Answers seem to be approaching 7. Answers seem to approach 0. Answers seem to approach —0. The temperature is decreasing at a rate of 4 degrees per minute after 2 minutes. Listen, 7th edition.

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