What are the problems of computing sinh(x) using its identity?

Question

unklerhaukus · Answer

$$\sinh x = \frac{e^x-e^{-x}}2$$

sheriph05 · Answer

Yea UnkleRhaukus.....I have this as an assignment (Numerical Analysis)i need to turn in tomorrow by 8am.and i have tried sourcing for useful info without success.

unklerhaukus · Answer

What is the question asking you to do?

unklerhaukus · Answer

Apply a particular numerical scheme?

sheriph05 · Answer

This is the question....
Using the definiton of sinh(x), discuss the problem of computing sinh(x)?

unklerhaukus · Answer

How are you computing it?

sheriph05 · Answer

No idea....That is why i posted the question here for you guys to provide me with a hint as this was not specified in the question

mathmate · Answer

hint:
expand e^x and e^-x as Taylor series, calculate sinh(x) in series form, and decide what would be a good way to calculate sinh(x), i.e. straight from definition in series form, or the modified series.
Discuss the computing efficiency, round-off errors and error bound in each case, with respect to different magnitude ranges of x.

sheriph05 · Answer

Thanks

mathmate · Answer

You're welcome! :)