Suppose the vector valued function r(t) (f(t), g(t), h(t)) is smooth on an interval containing the point t 0 The line tangent to r(t) at t t 0 is the line parallel to the tangent vector r '(t 0 ) that passes through (f(t 0 ), g(t 0 ), h(t 0 )) For each of the following functions, find an equation of the line tangent to the curve at t t 0 Choose an orientation for the line that is the same as the direction of r ' r(t) (2 cos t, 3 sin 2t, t) t 0 2

Question: Suppose the vector-valued function r(t) = (f(t), g(t), h(t)) is smooth on an interval containing the point t 0 . The line tangent to r(t)

Suppose the vector-valued function r(t) = (f(t), g(t), h(t)) is smooth on an interval containing the point t₀. The line tangent to r(t) at t = t₀ is the line parallel to the tangent vector r'(t₀) that passes through (f(t₀), g(t₀), h(t₀)). For each of the following functions, find an equation of the line tangent to the curve at t = t₀. Choose an orientation for the line that is the same as the direction of r'.

r(t) = (2 + cos t, 3 + sin 2t, t); t₀ = π/2

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