GATE CE 1998 | Calculus Question 46 | Engineering Mathematics

GATE CE 1998

MCQ (Single Correct Answer)

-0.3

The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if

$${f_x}\left( {a,\,b} \right) = {f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} < 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} > 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0,$$
$${f_{xx}}$$ and $${f_{yy}} < 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} = 0\,\,$$ at $$(a, b)$$

GATE CE 1998

MCQ (Single Correct Answer)

-0.3

A discontinuous real function can be expressed as

Taylor's series and Fourier's series

Taylor's series and not by Fourier's series

Neither Taylor's series nor Fourier's series

not by Taylor's series, but by Fourier's series

GATE CE 1998

MCQ (Single Correct Answer)

-0.3

The Taylor's series expansion of sin $$x$$ is ______.

$$1 - {{{x^2}} \over {2!}} + {{{x^4}} \over {4!}} - ......$$

$$1 + {{{x^2}} \over {4!}} + {{{x^4}} \over {4!}} + ......$$

$$x + {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} + ......$$

$$x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - ......$$

GATE CE 1997

MCQ (Single Correct Answer)

-0.3

If $$\varphi \left( x \right) = \int\limits_0^{{x^2}} {\sqrt t \,dt\,} $$ then $${{d\varphi } \over {dx}} = \_\_\_\_\_\_\_.$$

$$2\,{x^2}$$

$$\sqrt x $$

$$0$$

$$1$$

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Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Geomatics Engineering Or Surveying

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Reinforced Cement Concrete

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Materials and Specifications Tension Members Riveted Joints and Bolted Joints Welded Connections Eccentric Connections Compression Members Beams Plate Girder

Irrigation

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Environmental Engineering

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Engineering Mathematics

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