121616949-math.86 - 72 Chapter 4 Transcendental Functions...

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72 Chapter 4 Transcendental Functions 15. Find an equation for the tangent line to sin 2 ( x ) at x = π/ 3. 16. Find an equation for the tangent line to sec 2 x at x = π/ 3. 17. Find an equation for the tangent line to cos 2 x - sin 2 (4 x ) at x = π/ 6. 18. Find the points on the curve y = x + 2 cos x that have a horizontal tangent line. 19. Let C be a circle of radius r . Let A be an arc on C subtended by a central angle θ . Let B be the the chord of C whose endpoints are the endpoints of A . (Hence, B is also subtended by a central angle θ .) Let s be the length of A and let d be the length of B . Sketch a diagram of the situation and compute lim θ 0 + s/d . An exponential function has the form a x , where a is a constant; examples are 2 x , 10 x , e x . The logarithmic functions are the inverses of the exponential functions, that is, functions that “undo” the exponential functions, just as, for example, the cube root function “un- does” the cube function: 3 2 3 = 2. Note that the original function also undoes the inverse
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