# Elements of the Differential Calculus: With Examples and Applications

Ginn, 1891 - 258 sider

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Side 91 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Side 171 - F'P'+ P'F, by the definition of an ellipse. Take away from the first sum F'P + BF, and we have left PB ; take away from the second sum the equal amount F'A + P'F, and we have left P'A ; .-. PB=P'A; and the right triangles PAP...
Side 168 - Art. 162; T'PR= T'PF, and the tangent at any point of a parabola bisects the angle between the focal radius and the diameter through the given point. 164. To find the area of the sector of a parabola included between two focal radii. Take points of the parabola between the extremities of the bounding radii, and join them with the focus, thus dividing the area in question into smaller sectors, of which the sector FPP' in the figure of the last article may be taken as a type.
Side 172 - EXAMPLE. Prove that a tangent to an hyperbola bisects the angle between the focal radii drawn to the point of contact. 168. To find the area of a segment of a parabola cut off by a line perpendicular to the axis. Compare the required area with the area of the circumscribing rectangle. We can regard the...
Side 3 - Ja; representing a single quantity. It is to be noted that as an increment is a difference, it may be either positive or negative. 5. If a variable which changes its value according to some law can be made to approach some fixed, constant value as nearly as we please, but can never become equal to it, the constant is called the limit of the variable under the circumstances in question.
Side 37 - Show that u^a? - 3a?+6x+7 has neither a maximum or a minimum value ; and that is neither a maximum nor a minimum when x = 0. (5) A person in a boat, three miles from the nearest point of the beach, wishes to reach, in the shortest possible time, a place 5 -a five miles from that point, along the shore.