For the equation y = arcsinh(r/2), show that:(a) we can write y = ln (z+√²²+4),(b) for small r we have y r/8 to first order in z,(c) and that in the limit that a tends to zero we have }arcsinh(z/2) → 1/8.sin z

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Answered: For the equation y arcsinh (2/2), show…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Which statement is true? The function tan¹ (2)= arctan(x) = 0 has domainz € [-1,1] and range 0 € [-]. The function cot ¹(z) = arccot (x) = 0 has domainz € [-1, 1] and range 0 € [-]. The function csc ¹(x) = arccsc(20 = 8) has domain a € [-1, 1] and range 0 € [-]. The function sin-¹ (z) = arcsin(x) = has domainz € [-1, 1] and range 0 € [1,1] The function cos¹(x) = arccos(z) = 8 has domainz € [1,1] and range 0 € [1]
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For the equation y arcsinh (2/2), show that: -) we can write y-In (+√2²+4), ) for small z we have y r/8 to first order in 2, ) and that in the limit that z tends to zero we have }aresinh(a/2) → 1/8. sin z