3.6 - Webassign Answers

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3.6 Version 1 Answers

3.6 Version 2 Answers

3.6 Version 3 Answers

1. Prove the identity. Cosh(-x) = cosh x (This shows that cosh is an even function.) 2. Prove the identity. Cosh x + sinh x = e^x cosh x + sin x = 1/2 (e^x + e^-x) 3. Prove the identity. Sinh 2x = 2 sinh x cosh x Sinh 2x = sinh(x+ ) 4. ( 1+ tanh x )/(1-tanh x) = e^2x 5. If tanh x = 4/5, find the values of the other hyperbolic functions at x. 6. Prove the formulas given in this table for the derivates of the functions cosh, tanh , csch, sech, coth. Which of the following are proven correctly? (Select all that apply.) 7. Find the derivative. Simplify where possible. F(x) = tanh(5 + e^5x) 8. Find the derivative. Simplify where possible. F(x) = x sinh x – 9 cosh x 9. Find the derivative. Simplify where possible. G(x) = cosh(ln x) 10. Find the derivative. Simplify where possible. H(x) = ln(cosh(9x)) 11. Find the derivative. Simplify where possible. Y = x coth(7 + x^2) 12. Find the derivative. Simplify where possible. Y = e^cosh(4x) 13. Find the derivative. Simplify where possible. F(t) = sech^2(5e^t) 14. Find the derivative. Simplify where possible. G(x) = (5 – cosh x)/(5 + cosh x) 15. Find the derivative. Simplify where possible. Y = x arc tanh x + ln(1 – x^2)^1/2 16. Find the derivative. Simplify where possible. Y = x arc sinh(x/7) – (49 + x^2)^1/2 17. Show that d/dx arctan(tanh x) = sech 2x 18. Find the derivative. Simplify where possible. Y = arctanh (x)^1/2 19. Find the derivative. Simplify where possible. Arccoth(x^2 + 2)^1/2 20. If cosh x = 5/3 and x> 0, and find the values of the other hyperbolic functions at x.

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