Give an example each of the following. Justify your choice of examples. i) A non-trivial set in Euclidean space 2 R which is not path connected. ii) A vector-valued function 4 3 :f R → R for which the second order derivative exists. iii) A Lebesgue integrable function which is not differentiable.
Vector Arithmetic
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, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.
Vector Calculus
Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
Give an example each of the following. Justify your choice of examples.
i) A non-trivial set in Euclidean space 2 R which is not path connected.
ii) A
:f R → R for which the second order derivative exists.
iii) A Lebesgue
Step by step
Solved in 2 steps
