Which one of the following functions is continuous at x = 3?
A. \[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {2,}&{{\text{if}}}&{{\text{x}} = 3} \\ {{\text{x}} - 1,}&{{\text{if}}}&{{\text{x}} > 3} \\ {\frac{{{\text{x}} + 3}}{3},}&{{\text{if}}}&{{\text{x}} < 3} \end{array}} \right.\]
B. \[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {4,}&{{\text{if}}}&{{\text{x}} = 3} \\ {8 - {\text{x,}}}&{{\text{if}}}&{{\text{x}} \ne 3} \end{array}} \right.\]
C. \[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {{\text{x}} + 3,}&{{\text{if}}}&{{\text{x}} \leqslant 3} \\ {{\text{x}} - 4,}&{{\text{if}}}&{{\text{x}} > 3} \end{array}} \right.\]
D. $${\text{f}}\left( {\text{x}} \right) = \frac{1}{{{{\text{x}}^3} - 27}},\,{\text{if}}\,{\text{x}} \ne 3$$
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. \[ - 1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
Join The Discussion