1 The general solution of the equation = (1+ y²) cos x is y(x) = tan (C + sin x). With the initial condition y(0) = 0, the solution y(x) = tan (sin x) is well behaved. But with y(0) = 2.6 the solution y(x) = tan (tan ¯ 1 (2.6) + sin x) has a vertical asymptote at x=x-tan − 1 (2.6) = 0.37597. Use Euler's method to verify this fact empirically. Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h=0.05 y 0.25 h=0.005 0.3 0.35 (Do not round until the final answer. Then round to four decimal places as needed.)

1 The general solution of the equation = (1+ y²) cos x is y(x) = tan (C + sin x). With the initial condition y(0) = 0, the solution y(x) = tan (sin x) is well behaved. But with y(0) = 2.6 the solution y(x) = tan (tan ¯ 1 (2.6) + sin x) has a vertical asymptote at x=x-tan − 1 (2.6) = 0.37597. Use Euler's method to verify this fact empirically. Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h=0.05 y 0.25 h=0.005 0.3 0.35 (Do not round until the final answer. Then round to four decimal places as needed.)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.5: Derivatives Of Logarithmic Functions

Problem 47E

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