The arc-length function s(t) of a given path c(x) is defined by: s(t) = | |...

 

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The arc-length function s(t) of a given path c(x) is defined by: s(t) = | | || C (2)|| dar It measures the length of the path c(x) from x = a to x = t. The definitions of cosh and sinh are as follows: ex + e 2 sinh() _eze 2 cosh(t) They are related to parametrizing the hyperbola x² - y² = 1 in the same way that cos and sin are related to paramatrizing the circle x² + y² = 1. Thus they are called the hyperbolic trigonometric functions. 1. Compute the arclength function s(t) of c₁ (t) = (cos(t), sin(t), t) with a = 0. 2. Compute the arclength function s(t) of c₂ (t) = (cosh(t), sinh(t), t) with a = 0. The arc-length function s(t) of a given path c(x) is defined by: s(t) = | | || C (2)|| dar It measures the length of the path c(x) from x = a to x = t. The definitions of cosh and sinh are as follows: ex + e 2 sinh() _eze 2 cosh(t) They are related to parametrizing the hyperbola x² - y² = 1 in the same way that cos and sin are related to paramatrizing the circle x² + y² = 1. Thus they are called the hyperbolic trigonometric functions. 1. Compute the arclength function s(t) of c₁ (t) = (cos(t), sin(t), t) with a = 0. 2. Compute the arclength function s(t) of c₂ (t) = (cosh(t), sinh(t), t) with a = 0.

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