Calculus: Analytic Geometry and Calculus, with Vectors

446 Trigonometric functions for which (2) holds, then there must be constants I and B for which (1) holds. The latter and more d ...

8.1 Trigonometric functions and their derivatives 447 Do this. Then adapt the method of the preceding problem to show that ify i ...

448 Trigonometric functions In case m = n, and in other cases where lim m=0, m,n-.roW2 lim S,nn = 27rah, m,n- m the right member ...

8.2 Trigonometric integrands 449 foundation of human experience and that things not closely related to polynomials are more ethe ...

450 Trigonometric functions to an interval containing none of these points, we can use the funda- mental formula f [u(x)]-'u'(x) ...

8.2 Trigonometric integrands 451 the numerator and denominator of (sec x)/1 by the implausible factor sec x + tan x. We dispose ...

452 Trigonometric functions Students are frequently called upon to realize that the formula /1 +cos2x 2 1 + 2 cos2x +cost2x cos4 ...

8.2 Trigonometric integrands 453 is rendered manageable by replacing the factor cos3 x by the last member of the formula cos3 x ...

454 Trigonometric functions Instead of inviting attention to problems of this nature, we present prob- lems more likely to promo ...

8.2 Trigonometric integrands 455 must be a constant, but they do not imply that this constant must be zero. The identity x 1+tan ...

456 Putting (5) in the form Trigonometric functions (6) Q(tl,t2) =(I ) R(t2- tl) shows that a sinusoidal current having maximum ...

8.2 Trigonometric integrands 457 which is correct whenever p > -1 and q > -1. As usual, 0! = 1, 1! = 1, 2! = 1.2, 3! = 1.2 ...

458 Trigonometric functions for each n = 1, 2, 3,. It is true (and is easy to surmise) that, for each x, JxIn/n! --> 0 as n - ...

8.3 Inverse trigonometric functions 459 in D1 for which f(x) = y. Then we can introducea function fl, which is different from f ...

460 Trigonometric functions fl has an inverse defined over R. Since we must prove that fl' is differ- entiable, we introduce dif ...

8.3 Inverse trigonometric functions 461 R being the closed interval -1 <- y 5 1. When we are called upon to select a domain D ...

462 Trigonometric functions The inverse cosine is the inverse of the function fl, with domain 0 5 x < it and range -1 < x ...

8.3 Inverse trigonometric functions 463 The inverse cotangent is the inverse of the function fl, with domain 0 < x < 7r an ...

464 Trigonometric functions The graph of y = csc x presents the same difficulty that the graph of y = sec x presented. The best ...

8.3 Inverse trigonometric functions 465 which involves completing a square. It may be time to renew the idea that normal persons ...