Question

In the usual notation, the value of $\Delta \nabla $ is equal to
A. $\Delta - \nabla $
B. $\Delta + \nabla $
C. $\nabla - \Delta $
D. none of these

Answer 1

Hint: In this question, we need to find the value of $\Delta \nabla $. We know that Del, or nabla, is a vector differential operator used in mathematics, particularly in vector calculus, and is generally denoted by the nabla symbol. We will find this value by using the delta of difference between two functions to get the desired value.

Complete step by step solution:
Now we know that Calculus is a branch of mathematics that studies continuous change. It can be changed in any way, such as the limit or the function. The term delta is commonly used to denote a change in values or the difference between two values of a variable and the term nabla is the collection of all its partial derivatives into a vector.
Now,
$\Delta \nabla f\left( x \right) = \Delta \left[ {f\left( x \right) - f\left( {x - h} \right)} \right] \\ \Rightarrow \Delta f\left( x \right) - \Delta f\left( {x - h} \right) \\ \Rightarrow \Delta f\left( x \right) - \left[ {f\left( x \right) - f\left( {x - h} \right)} \right] \\ \Rightarrow \Delta f\left( x \right) - \nabla f\left( x \right)$
Therefore, $\Delta \nabla = \Delta - \nabla $

Option ‘A’ is correct

Additional Information: Delta is a four-letter Greek letter that means "change." In mathematics, it is used as a number, function, and equation. Calculus, on the other hand, is a branch of mathematics that deals with continuous changes in variables. The nebla is a vector operator, with each vector element representing the partial derivative, or slope, of the function being operated on in one of three spatial directions.

Note: In simple words, Delta is denoted by $\Delta $and the nebla is denoted by $\nabla $. On the other hand, delta and nabla are operators used in mathematics. Also, delta means the amount of change of a quantity from previous number to present number whereas nebla is used to express the gradient and other vector derivatives.