1
GATE CE 2000
+2
-0.6
The Taylor series expansion of sin $$x$$ about $$x = {\pi \over 6}$$ is given by
A
$${1 \over 2} + {{\sqrt 3 } \over 2}\left( {x - {\Pi \over 6}} \right) - {1 \over 4}{\left( {x - {\Pi \over 6}} \right)^2} - {{\sqrt 3 } \over {12}}{\left( {x - {\Pi \over 6}} \right)^3} + - -$$
B
$$x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - -$$
C
$${{x - {\Pi \over 6}} \over {1!}} - {{{{\left( {x - {\Pi \over 6}} \right)}^3}} \over {3!}} + {{{{\left( {x - {\Pi \over 6}} \right)}^5}} \over {5!}} - {{{{\left( {x - {\Pi \over 6}} \right)}^7}} \over {7!}} + - - - -$$
D
$${1 \over 2}$$
2
GATE CE 2000
+2
-0.6
Limit of the function
$$f\left( x \right) = {{1 - {a^4}} \over {{x^4}}}\,\,as\,\,x \to \infty$$ is given by
A
$$1$$
B
$${e^{ - {a^4}}}$$
C
$$\infty$$
D
$$0$$
3
GATE CE 2000
+2
-0.6
If $$f\left( {x,y,z} \right) =$$
$${\left( {{x^2} + {y^2} + {z^2}} \right)^{{\raise0.5ex\hbox{\scriptstyle { - 1}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}},$$ $${{{\partial ^2}f} \over {\partial {x^2}}} + {{{\partial ^2}f} \over {\partial {y^2}}} + {{{\partial ^2}f} \over {\partial {z^2}}}$$ is equal to _______.
A
$$0$$
B
$$1$$
C
$$2$$
D
$$- 3{\left( {{x^2} + {y^2} + {z^2}} \right)^{{\raise0.5ex\hbox{\scriptstyle { - 5}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Environmental Engineering
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Medical
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