A function f(x) is defined as
\[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}}
{{{\text{e}}^x}}&{{\text{x}} < 1} \\
{\ln {\text{x}} + {\text{a}}{{\text{x}}^2} + {\text{bx}},}&{{\text{x}} \geqslant 1}
\end{array}} \right.\]
where x\[ \in \] R which one of the following statements is TRUE?
A. f(x) is NOT differentiable at x = 1 for any values of a and b
B. f(x) is differentiable at x = 1 for the unique values of a and b
C. f(x) is differentiable at x = 1 for all the values of a and b such that a + b = e
D. f(x) is differentiable at x = 1 for all values of a and b
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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