Unformatted text preview: √ 17. Show that, if x2 ≥ 1, then x − x2 − 1 ≤ 1. 18. Show that tanh−1 x = 19. Show that
(7.9.3) 1 1+x ln , 2 1−x −1 < x < 1. 25. Sketch the graph of y = sech x, giving: (a) the extreme values; (b) the points of inﬂection; and (c) the concavity. 26. Sketch the graphs of (a) y = coth x, (b) y = csch x. 27. Graph y = sinh x and y = sinh−1 x in the same coordinate system. Find all points of inﬂection. 28. Sketch the graphs of (a) y = cosh−1 x, (b) y = tanh−1 x. 29. Given that tan φ = sinh x, show that dφ = sech x. (a) dx (b) x = ln ( sec φ + tan φ ). dx (c) = sec φ . dφ 30. The region bounded by the graph of y = sech x between x = −1 and x = 1 is revolved about the x-axis. Find the volume of the solid that is generated. Calculate the integral. 31. tanh x dx. sech x dx. sech3 x tanh x dx. 32. 34. 36. coth x dx. csch x dx. x sech2 x2 dx. d 1 ( sinh−1 x) = √ , 2+1 dx x x real. 20. Show that 33.
(7.9.4) d 1 ( cosh−1 x) = √ , dx x2 − 1 x > 1. 35. 444
37. 39. CHAPTER 7 THE TRANSCENDENTAL FUNCTIONS tanh x ln ( cosh x) dx. sech2 x dx. 1 + tanh x 38. 40. 1 + tanh x dx. cosh2 x tanh x sech x dx.
5 2 (a) Show that v (t ) = mg tanh k gk t m In Exercis...
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.
- Spring '10
- Hyperbolic Functions