1
GATE ECE 2015 Set 1
+1
-0.3
A function $$f\left( x \right) = 1 - {x^2} + {x^3}\,\,$$ is defined in the closed interval $$\left[ { - 1,1} \right].$$ The value of $$x,$$ in the open interval $$(-1,1)$$ for which the mean value theorem is satisfied, is
A
$$- {1 \over 2}$$
B
$$- {1 \over 3}$$
C
$${1 \over 3}$$
D
$${1 \over 2}$$
2
GATE ECE 2014 Set 4
+1
-0.3
The series $$\sum\limits_{n = 0}^\infty {{1 \over {n!}}\,}$$ converges to
A
$$2$$ $$ln$$ $$2$$
B
$${\sqrt 2 }$$
C
$$2$$
D
$$e$$
3
GATE ECE 2014 Set 3
Numerical
+1
-0
The maximum value of the function $$\,f\left( x \right) = \ln \left( {1 + x} \right) - x$$ (where $$x > - 1$$ ) occurs at $$x=$$________.
4
GATE ECE 2014 Set 3
+1
-0.3
If $$z=xy$$ $$ln(xy),$$ then
A
$$x{{\partial z} \over {\partial x}} + y{{\partial z} \over {\partial y}} = 0$$
B
$$y{{\partial z} \over {\partial x}} = x{{\partial z} \over {\partial y}}$$
C
$$x{{\partial z} \over {\partial x}} = y{{\partial z} \over {\partial y}}$$
D
$$y{{\partial z} \over {\partial x}} + x{{\partial z} \over {\partial y}} = 0$$
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