The hyperbolic cosine function, denoted cosh(x)\cosh\left(x\right... | Study Prep in Pearson
The hyperbolic cosine function, denoted cosh(x)\cosh\left(x\right..…
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SOLVED:The hyperbolic cosine function is defined by cosh(x)= (e^x e^-x) / 2 . Prove that cosh is an even function.
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The hyperbolic functions cosh z and sinhz are defined as follows: coshz=(e^z e^-z)/(2) and sinhz=(e^z-e^-z)/(2) for any z, real or complex. (a) Sketch the behavior of both functions over a suitable range of real values of z. (b) Show that coshz=cos(i z). What is the corresponding relation for sinhz ? (c) What are the derivatives of cosh z and sinhz ? What about their integrals? ( 𝐝 ) Show that cosh^2 z-sinh^2 z=1 (e) Show that ∫d x / √(1 x^2)=arcsinh x. [Hint: One way to do this is to mak
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