Consider the space curve C given by the vector function f(t) = (t² + 1)i + (2t4 – 3t2)j +t³k where t e [-1,2]. Í(t) %3D (a) By inspection, state and give a brief reason in words, whether or not C is smooth. (b) By inspection, state and give a brief reason in words, whether or not the tangent line to C at the point (1,0,0) exists. (You may use normal print f or “the vector function" and f' or “the derivative" for f and f' respectively in typing up your brief response when referring to the function and its derivative, respectively. Give statements like, for example “The r-component of f is not continuous", or “The z-component of the deriva- tive is not zero when t = 0", etc. You are not required to type in the actual %3D algebraic expression.)

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.