Show that 793 1 1x ln 2 1x 1 x 1 25 sketch the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online