## Elements of the Differential and Integral Calculus |

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### Common terms and phrases

altitude angle approaches the limit approaches zero assume asymptote axis center of curvature circle concave upwards consider constant convergent coordinates corresponding cosx critical value cycloid cylinder denoted differential equation dv dx dx dx dx dx dy dy dx ellipse equal evolute EXAMPLES expression Find the area Find the equation formula Fourth step fraction gives max graph Hence hypocycloid implicit function increases without limit increment independent variable indeterminate form infinite integral intersection limit zero logarithm maxima and minima minimum values normal parabola parallel parametric equations partial derivatives plane point of inflection polar radius of curvature rate of change rational rational function rectangular result Rolle's Theorem roots Second step Show sin2 slope Solution solving Substituting subtangent surface Theorem of Mean Third step velocity

### Popular passages

Page 52 - 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 39 - x". It is not "dy" divided by "dx" or "d" multiplied by "y" divided by "d" multiplied by "x." In precise mathematical terms a derivative of a function is the limit of the ratio of the increment of the function to the increment of the independent variable when the latter increment varies and approaches zero as a limit.

Page 17 - The angle subtended at the center of a circle by an arc equal in length to a radius of the circle.

Page 109 - Similarly, the derivative of the second derivative is called the third derivative ; and so on to the nth derivative.

Page 130 - Assuming that the strength of a beam with rectangular cross section varies directly as the breadth and as the square of the depth, what are the dimensions of the strongest beam that can be sawed out of a round log whose diameter is d ? Solution.

Page 175 - Differentiate the numerator for a new numerator and the denominator for a new denominator.* The...

Page 19 - What is the ratio of their radii ? of their apothems ? of their perimeters ? of their areas ? 5. The diameters of two circles are d and d' respectively. What is the ratio of their radii ? of their circumferences ? of their areas ? 6. If the number of sides of a regular inscribed polygon is indefinitely increased, what is the limit of the apothem ? of each side ? of the perimeter ? of the area ? of the angle at the center ? of each angle of the polygon ? 7. How do you find the area of a regular polygon...

Page 131 - Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm is -*- cm.

Page 12 - By the definition of a function we see that the area of a square is a function of the length of a side and the distance that a falling body travels is a function of the time it falls.

Page 50 - The summation of the product of a constant and a variable is equal to the product of the constant and the summation of that variable: A collection, class, or listing of mathematical objects is called a set.