Curl of vector \[\overrightarrow {\rm{F}} = {{\rm{x}}^2}{{\rm{z}}^2}{\rm{\hat i}} - 2{\rm{x}}{{\rm{y}}^2}{\rm{z\hat j}} + 2{{\rm{y}}^2}{{\rm{z}}^3}{\rm{\hat k}}\] is
A. \[\left( {4{\rm{y}}{{\rm{z}}^3} + 2{\rm{x}}{{\rm{y}}^2}} \right){\rm{\hat i}} + 2{{\rm{x}}^2}{\rm{z\hat j}} - 2{{\rm{y}}^2}{\rm{z\hat k}}\]
B. \[\left( {4{\rm{y}}{{\rm{z}}^3} + 2{\rm{x}}{{\rm{y}}^2}} \right){\rm{\hat i}} - 2{{\rm{x}}^2}{\rm{z\hat j}} - 2{{\rm{y}}^2}{\rm{z\hat k}}\]
C. \[2{\rm{x}}{{\rm{z}}^2}{\rm{\hat i}} - 4{\rm{xyz\hat j}} + 6{{\rm{y}}^2}{{\rm{z}}^2}{\rm{\hat k}}\]
D. \[2{\rm{x}}{{\rm{z}}^2}{\rm{\hat i}} + 4{\rm{xyz\hat j}} + 6{{\rm{y}}^2}{{\rm{z}}^2}{\rm{\hat k}}\]
Answer: Option A
This Question Belongs to Engineering Maths >> Calculus
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 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
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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