MHT CET · Maths · Mathematical Reasoning
In the usual notation the value of \(\Delta \nabla\) is equal to
- A \(\Delta-\nabla\)
- B \(\Delta+\nabla\)
- C \(\nabla-\Delta\)
- D None of the above
Answer & Solution
Correct Answer
(A) \(\Delta-\nabla\)
Step-by-step Solution
Detailed explanation
Now, \(\Delta \nabla f(x)=\Delta[f(x)-f(x-h)]\)
\(=\Delta f(x)-\Delta f(x-h) \)
\( =\Delta f(x)-[f(x)-f(x-h)] \)
\( =\Delta f(x)-\nabla f(x) \)
\( \Delta \nabla =\Delta-\nabla\)
\(=\Delta f(x)-\Delta f(x-h) \)
\( =\Delta f(x)-[f(x)-f(x-h)] \)
\( =\Delta f(x)-\nabla f(x) \)
\( \Delta \nabla =\Delta-\nabla\)
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