For a small value of h, the Taylor series expansion for f(x + h) is
A. \[{\text{f}}\left( {\text{x}} \right) + {\text{hf}}'\left( {\text{x}} \right) + \frac{{{{\text{h}}^2}}}{2}{\text{f}}''\left( {\text{x}} \right) + \frac{{{{\text{h}}^3}}}{3}{\text{f}}''\left( {\text{x}} \right) + \,...\,\infty \]
B. \[{\text{f}}\left( {\text{x}} \right) - {\text{hf}}'\left( {\text{x}} \right) + \frac{{{{\text{h}}^2}}}{{2!}}{\text{f}}''\left( {\text{x}} \right) - \frac{{{{\text{h}}^3}}}{{3!}}{\text{f}}''\left( {\text{x}} \right) + \,...\,\infty \]
C. \[{\text{f}}\left( {\text{x}} \right) + {\text{hf}}'\left( {\text{x}} \right) + \frac{{{{\text{h}}^2}}}{{2!}}{\text{f}}''\left( {\text{x}} \right) + \frac{{{{\text{h}}^3}}}{{3!}}{\text{f}}''\left( {\text{x}} \right) + \,...\,\infty \]
D. \[{\text{f}}\left( {\text{x}} \right) - {\text{hf}}'\left( {\text{x}} \right) + \frac{{{{\text{h}}^2}}}{2}{\text{f}}''\left( {\text{x}} \right) - \frac{{{{\text{h}}^3}}}{3}{\text{f}}''\left( {\text{x}} \right) + \,...\,\infty \]
Answer: Option C
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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