If for non-zero x, \[{\rm{af}}\left( {\rm{x}} \right) + {\rm{bf}}\left( {\frac{1}{{\rm{x}}}} \right) = \frac{1}{{\rm{x}}} - 25\] where a ≠ b then \[\int\limits_1^2 {{\rm{f}}\left( {\rm{x}} \right){\rm{dx}}} \] is
A. \[\frac{1}{{{{\rm{a}}^2} - {{\rm{b}}^2}}}\left[ {a\left( {\ln 2 - 25} \right) + \frac{{47{\rm{b}}}}{2}} \right]\]
B. \[\frac{1}{{{{\rm{a}}^2} - {{\rm{b}}^2}}}\left[ {a\left( {2\ln 2 - 25} \right) - \frac{{47{\rm{b}}}}{2}} \right]\]
C. \[\frac{1}{{{{\rm{a}}^2} - {{\rm{b}}^2}}}\left[ {a\left( {2\ln 2 - 25} \right) + \frac{{47{\rm{b}}}}{2}} \right]\]
D. \[\frac{1}{{{{\rm{a}}^2} - {{\rm{b}}^2}}}\left[ {a\left( {\ln 2 - 25} \right) - \frac{{47{\rm{b}}}}{2}} \right]\]
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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