Elementary Analysis |
Contents
| 111 | |
| 114 | |
| 115 | |
| 116 | |
| 117 | |
| 123 | |
| 124 | |
| 127 | |
| 13 | |
| 16 | |
| 21 | |
| 28 | |
| 30 | |
| 35 | |
| 36 | |
| 41 | |
| 45 | |
| 46 | |
| 47 | |
| 50 | |
| 54 | |
| 63 | |
| 70 | |
| 77 | |
| 83 | |
| 91 | |
| 100 | |
| 129 | |
| 132 | |
| 135 | |
| 136 | |
| 139 | |
| 140 | |
| 143 | |
| 146 | |
| 151 | |
| 156 | |
| 161 | |
| 162 | |
| 167 | |
| 175 | |
| 182 | |
| 194 | |
| 201 | |
| 207 | |
| 216 | |
Other editions - View all
Elementary Analysis (1910) Percey Franklyn Smith,William Anthony Granville No preview available - 2008 |
Common terms and phrases
abscissas algebraic ANALYTIC GEOMETRY axis Calculus circle common logarithm concave upwards cone coördinates cos² cylinder definite integral derivative distance dv dx dx dx dx dx dy dy dx equal example figure Find the area Find the equation Find the slope formula Fourth step function GEOMETRY given condition gives graph Hence intercept length limit line joining line passing logarithms maxima and minima middle point natural logarithms negative ordinates P₁ parabola Plot the locus point moves points of inflection points of intersection positive problem radians radius real numbers rectangle result right triangle sec² Second step sides sin x sin² Solution Solving square straight line Substituting symmetrical with respect tangent Theorem Third step triangle whose vertices Va² variable volume x-axis y-axis y₁ zero Δυ Пх
Popular passages
Page 63 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 76 - be denoted by /<;, we find for the locus 4 ax = k or 4 ax = — k. 13. A point moves so that the sum of the squares of its distances from two fixed points is constant. Prove that the locus is a circle.
Page 75 - Find the equation of the locus of a point which moves so that its distances from (8, 0) and (2, 0) are always in a constant ratio equal to 2.
Page 76 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 49 - A conic section is the locus of a point whose distances from a fixed point and a fixed line are in a constant ratio. 4. Show that every conic is represented by an equation of the second degree in x and y. Hint. Take Y Y' to coincide with the fixed line, and draw XX
Page 74 - A point moves so that the difference of the squares of its distances from two fixed points is constant. Show that the locus is a straight line. Hint. Draw XX' through the fixed points, and YY/ through their middle point.
Page 116 - The derivative of the product of two functions is equal to the first function times the derivative of the second plus the second times the derivative of the first.
Page 26 - Show that the area of the triangle whose vertices are (4, 6), (2, — 4), (—4, 2) is four times the area of the triangle formed by joining the middle points of the sides.
Page 118 - The derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
Page 4 - In any triangle, the square of any side is equal to the sum of the squares of the two other sides, diminished by twice the rectangle of these sides multiplied by the cosine of the included angle.