Let \[\phi \] be an arbitrary smooth real valued scalar function and V be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following is an identity?
A. \[{\text{Curl}}\left( {\phi \overrightarrow {\text{V}} } \right) = \nabla \left( {\phi {\text{Div}}\overrightarrow {\text{V}} } \right)\]
B. \[{\text{Div }}\overrightarrow {\text{V}} = 0\]
C. \[{\text{Div Curl }}\overrightarrow {\text{V}} = 0\]
D. \[{\text{Div}}\left( {\phi \overrightarrow {\text{V}} } \right) = \phi {\text{Div }}\overrightarrow {\text{V}} \]
Answer: Option C
The Taylor series expansion of 3 sinx + 2 cosx is . . . . . . . .
A. 2 + 3x - x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
B. 2 - 3x + x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
C. 2 + 3x + x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
D. 2 - 3x - x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
A. 0
B. \[\infty \]
C. \[\frac{1}{2}\]
D. \[ - \infty \]
A. \[1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
B. \[ - 1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
C. \[1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
D. \[ - 1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
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