In practice it is often easier to rewrite the function.
Sketch the curve represented by the vector-valued function and give the orientation of the curve.
#26 r(t)=
#34 r(t)=
jttit 22 1kt
tjti2
sin4cos3
kt
tjti2
sin4cos3
Definition of the Limit of a Vector-Valued Function
Definition of Continuity of a Vector-Valued Function
Section 11.2
• Differentiation and Integration of Vector-Valued Functions.
Definition of the Derivative of a Vector-Valued Function
Theorem 12.1 Differentiation of Vector-Valued Functions
Theorem 12.2 Properties of the Derivative
Definition of Integration of Vector-Valued Functions
Smooth Functions
• A vector valued function, r, is smooth on an open interval I if the derivatives of the components are continuous on I and r’ 0 for any value of t in the interval I.
#30 Find the open interval(s) on which the curve is smooth.