Preliminary Questions

Question 13.52

State the three forms of the Product Rule for vector-valued functions.

In Questions 2–6, indicate whether the statement is true or false, and if it is false, provide a correct statement.

Question 13.53

The derivative of a vector-valued function is defined as the limit of the difference quotient, just as in the scalar-valued case.

Question 13.54

There are two Chain Rules for vector-valued functions: one for the composite of two vector-valued functions and one for the composite of a vector-valued and a scalar-valued function.

Question 13.55

The terms “velocity vector” and “tangent vector” for a path r(t) mean one and the same thing.

Question 13.56

The derivative of a vector-valued function is the slope of the tangent line, just as in the scalar case.

Question 13.57

The derivative of the cross product is the cross product of the derivatives.

Question 13.58

State whether the following derivatives of vector-valued functions r1(t) and r2(t) are scalars or vectors: