1
GATE ECE 2009
+2
-0.6
The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi$$ is given by
A
$$1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
B
$$- 1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
C
$$1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
D
$$- 1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
2
GATE ECE 2008
+2
-0.6
The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line segment from the point $$(0,0)$$ to the point $$(1,2)$$ in the $$xy$$ -plane is
A
$$33$$
B
$$35$$
C
$$40$$
D
$$56$$
3
GATE ECE 2008
+2
-0.6
In the Taylor series expansion of $${e^x} + \sin x$$ about the point $$x = \pi ,$$ the coefficient of $${\left( {x = \pi } \right)^2}$$ is
A
$${e^\pi }$$
B
$$0.5$$ $${e^\pi }$$
C
$${e^\pi }$$ $$+1$$
D
$${e^\pi }$$ $$-1$$
4
GATE ECE 2007
+2
-0.6
Consider the function $$\,f\left( x \right) = {x^2} - x - 2.\,$$ The maximum value of $$f(x)$$ in the closed interval $$\left[ { - 4,4} \right]\,$$
A
$$18$$
B
$$10$$
C
$$-2.25$$
D
indeterminate
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