Elementary Functions and Applications |
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Page x
... Tangent Line .. 34. Graph of the Quadratic Function ax2 + bx + c . 35. Empirical Data Problems .. 36. The Function x " . 94 98 104 107 Reciprocals .. 38. Graph of x2 , n > 1 37. Tables of Squares , Cubes , Square Roots , Cube Roots ...
... Tangent Line .. 34. Graph of the Quadratic Function ax2 + bx + c . 35. Empirical Data Problems .. 36. The Function x " . 94 98 104 107 Reciprocals .. 38. Graph of x2 , n > 1 37. Tables of Squares , Cubes , Square Roots , Cube Roots ...
Page xii
... Tangent and Normal Lines . 281 101. Problems in Maxima and Minima .. 285 102. Related Rates ... 289 103. Small Errors . 291 104. Approximate value of f ( x + Ax ) 296 CHAPTER VII INTEGRATION 105. Introduction . 301 106. Area under a ...
... Tangent and Normal Lines . 281 101. Problems in Maxima and Minima .. 285 102. Related Rates ... 289 103. Small Errors . 291 104. Approximate value of f ( x + Ax ) 296 CHAPTER VII INTEGRATION 105. Introduction . 301 106. Area under a ...
Page 94
... Tangent Line . A generaliza- tion of the idea of instantaneous velocity , which may be de- scribed as the rate of change of the distance s with respect to the time t , is given in the DEFINITION . The rate of change of y with respect to ...
... Tangent Line . A generaliza- tion of the idea of instantaneous velocity , which may be de- scribed as the rate of change of the distance s with respect to the time t , is given in the DEFINITION . The rate of change of y with respect to ...
Page 95
... tangent to the curve at P is the limiting position of the secant PQ as Q moves along the curve and approaches P. The ... tangent PT , and the slope of PQ approaches that of PT . Hence , The rate of change of y with respect to x is ...
... tangent to the curve at P is the limiting position of the secant PQ as Q moves along the curve and approaches P. The ... tangent PT , and the slope of PQ approaches that of PT . Hence , The rate of change of y with respect to x is ...
Page 96
... tangent line at any point . If x = 0 , we have m = O , so that the parabola which is the graph of ( 3 ) is tangent to the x - axis at the origin . For a given value of x , the larger the value of a , the larger also is the slope of the ...
... tangent line at any point . If x = 0 , we have m = O , so that the parabola which is the graph of ( 3 ) is tangent to the x - axis at the origin . For a given value of x , the larger the value of a , the larger also is the slope of the ...
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Other editions - View all
Elementary Functions and Applications (Classic Reprint) Arthur Sullivan Gale No preview available - 2018 |
Common terms and phrases
abscissas algebraic altitude angle approximately arithmetic mean asymptote average rate ax² Ay/Ax ball class intervals coefficient common logarithms computed constant Construct the graph coördinates curve denote determined deviation distance equal EXAMPLE EXERCISES exponential function feet per second Find the equation find the value fraction frequency function Hence horizontal inches increases integral intercept inverse inverse function law of cosines law of sines logarithms maximum mean measurements miles an hour minimum point negative obtained ordinates P₁ pairs of values parabola plane Plot the graph point of inflection polynomial positive probable error properties quadrant quadratic function radians radius rate of change ratio relation relative error represented right triangle roots Section sides sin² slope solution Solve square straight line Substituting table of values tangent line temperature Theorem tion variable velocity vertical volume weight whence x-axis y-axis
Popular passages
Page 368 - This is the same as the number of permutations of n things taken r at a time, and hence r!C(»,r) = P(«,r) '-- It is interesting to know that the number of combinations of n things taken r at a time is the same as the number of combinations of n things taken n — r at a time.
Page 223 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page xviii - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page xviii - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page 171 - A radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
Page 223 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Page 289 - Now all know that the intensity of illumination varies inversely as the square of the distance.
Page 155 - It is found that the quantity of work done by a man in an hour varies directly as his pay per hour and inversely as the square root of the number of hours he works per day. He can finish a piece of work in six days when working 9 hours a day at Is.
Page 181 - You have learned that the tangent of an acute angle of a right triangle is the ratio of the side opposite the angle to the side adjacent to the angle.
Page 368 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.