The polynomial p(x) = x5 + x + 2 has
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Engineering Maths · all questionsCalculus
Calculus
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A function y = 5x2 + 10x is defined over an open interval x = (1, 2). At least at one point in this interval, is exactly
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Let x and y be two vectors in a 3 dimensional space and <x, y> denote their dot product. Then the determinant det \left[ {\begin{array}{*{20}{c}}
{ < {\text{x}},{\text{x}} > }&{ < {\text{x}},{\text{y}} > } \\
{ < {\text{y}},{\text{x}} > }&{ < {\text{y}},{\text{y}} > }
\end{array}} \right].
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equal to
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For a vector E, which one of the following statements is NOT TRUE?
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Which one of the following functions is continuous at x = 3?
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If A(0, 4, 3), B(0, 0, 0) and C(3, 0, 4) are three points defined in x, y, zeo-ordinate system, then which of the following vector is perpendicular to both vectors and
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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 R which one of the following statements is TRUE?
{\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 R which one of the following statements is TRUE?
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The inner (dot) product of two non zero vectors and is zero. The angle (degrees) between the two vectors is
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Let f(x) = ex + x2 for real x. From among the following, choose the Taylor series approximation of f(x) around x = 0, which includes all powers of x less than or equal to 3,
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For the function e-x, the linear approximation around x = 2 is
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The infinite series converges to
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If the vector function
is irrotational, then the values of the constants k1, k2 and k3 respectively, are
is irrotational, then the values of the constants k1, k2 and k3 respectively, are
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Consider a differentiable function f(x) on the set of real numbers such that f(-1) = 0 and |f'(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x [-2, 2]?
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The curve y = x4 is
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Which one of the following functions is strictly bounded?
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A parametric curve defined by in the range 0 ≤ u ≤ 1 is rotated about the x-axis by 360°. Area of the surface generated is
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Let {\rm{g}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}}
{ - {\rm{x,}}}&{{\rm{x}} \le 1}\\
{{\rm{x}} + 1,}&{{\rm{x}} \ge 1}
\end{array}} \right. and {\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}}
{1 - {\rm{x,}}}&{{\rm{x}} \le 0}\\
{{{\rm{x}}^2},}&{{\rm{x}} > 0}
\end{array}} \right..
Consider the composition of f and g i.e. (fog) (x) = f(g(x)). The number of discontinuities in (fog) (x) present in the interval ( 0) is:
Consider the composition of f and g i.e. (fog) (x) = f(g(x)). The number of discontinuities in (fog) (x) present in the interval ( 0) is:
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What is equal to?
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A cubic polynomial with real coefficients
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