13.6 13.2: SUMMARY

• Limits, differentiation, and integration of vector-valued functions are performed componentwise.

• Differentation rules:

  • Sum Rule:

    738

  • Constant Multiple Rule: (c r(t))′ = c r′(t)

  • Chain Rule:

• Product Rules:

  

• The derivative r′(t₀) is called the tangent vector or velocity vector.

• If r′(t₀) is nonzero, then it points in the direction tangent to the curve at r(t₀). The tangent line has vector parametrization

  L(t) = r(t₀) + tr′(t₀)

• If , then R₁(t) = R₂(t) + c for some constant vector c.

• The Fundamental Theorem for vector-valued functions: If r(t) is continuous and R(t) is an antiderivative of r(t), then