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SOLVED: Find the arc length of the curve y = cosh X from x = 0 to x =

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SOLVED:The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a telephone wire, for example). It is defined as coshx=(e^x e^-x)/(2). a. Determine its end behavior by evaluating limcoshx and limx →-∞ coshx. b. Evaluate cosh 0. Use symmetry and part (a) to sketch a plausible graph for y=coshx.

SOLVED:Show that \cosh (x y)=\cosh x \cosh y \sinh x \sinh y for all real numbers x and y.

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