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The value of the integral $$\int\!\!\!\int\limits_D {3({x^2} + {y^2})dx\,dy}$$, where D is the shaded triangular region...
GATE ECE 2022
The function f(x) = 8loge x $$-$$ x2 + 3 attains its minimum over the interval [1, e] at x = __________. (Here loge x is...
GATE ECE 2022
Consider the two-dimensional vector field $$\overrightarrow F (x,y) - x\overrightarrow i + y\overrightarrow j$$, where...
GATE ECE 2022
The families of curves represented by the solution of the equation $${{dy} \over {dx}} = - {\left( {{x \over y}} \right... GATE ECE 2019 Taylor series expansion of$$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$arou... GATE ECE 2018 Let$$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where$$a$$and$$b$$are constants. If$${{\partial f} ...
GATE ECE 2018
How many distinct values of $$x$$ satisfy the equation $$sin(x)=x/2,$$ where $$x$$ is in radians ?
GATE ECE 2016 Set 2
The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}}$$ is equal ________.
GATE ECE 2016 Set 3
As $$x$$ varies from $$- 1$$ to $$3,$$ which of the following describes the behavior of the function $$f\left( x \righ... GATE ECE 2016 Set 2 Given the following statements about a function$$f:R \to R,$$select the right option:$$P:$$If$$f(x)$$is continuou... GATE ECE 2016 Set 1 The contour on the$$x-y$$plane, where the partial derivative of$${x^2} + {y^2}$$with respect to$$y$$is equal to th... GATE ECE 2015 Set 3 The value of$$\sum\limits_{n = 0}^\infty {n{{\left( {{1 \over 2}} \right)}^n}\,\,} $$is _______. GATE ECE 2015 Set 3 A function$$f\left( x \right) = 1 - {x^2} + {x^3}\,\,$$is defined in the closed interval$$\left[ { - 1,1} \right].$$... GATE ECE 2015 Set 1 The series$$\sum\limits_{n = 0}^\infty {{1 \over {n!}}\,} $$converges to GATE ECE 2014 Set 4 If$$z=xyln(xy),$$then GATE ECE 2014 Set 3 The maximum value of the function$$\,f\left( x \right) = \ln \left( {1 + x} \right) - x$$(where$$x &gt; - 1$$) occu... GATE ECE 2014 Set 3 The value of$$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^x}\,\,$$is GATE ECE 2014 Set 2 For$$0 \le t &lt; \infty ,$$the maximum value of the function$$f\left( t \right) = {e^{ - t}} - 2{e^{ - 2t}}\,$$occ... GATE ECE 2014 Set 2 If$$\,{e^y} = {x^{1/x}}\,\,$$then$$y$$has a GATE ECE 2010 Which of the following function would have only odd powers of$$x$$in its Taylor series expansion about the point$$x=0...
GATE ECE 2008
For real values of $$x,$$ the minimum value of function $$f\left( x \right) = {e^x} + {e^{ - x}}\,\,$$ is
GATE ECE 2008
For $$\left| x \right| &lt; &lt; 1,\,\cot \,h\left( x \right)\,\,\,$$ can be approximated as
GATE ECE 2007
For the function $${e^{ - x}},$$ the linear approximation around $$x=2$$ is
GATE ECE 2007
The following plot shows a function $$y$$ which varies linearly with $$x$$. The value of the integral $$\,\,{\rm I} = \i... GATE ECE 2007$$\mathop {Lim}\limits_{\theta \to 0} {{\sin \left( {\theta /2} \right)} \over \theta }\,\,\,$$is GATE ECE 2007 The value of the integral$$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{$\scriptst... GATE ECE 2005 The curve given by the equation $${x^2} + {y^2} = 3axy$$ is GATE ECE 1997 The third term in the taylor's series expansion of $${e^x}$$ about $$'a'$$ would be ________. GATE ECE 1995 By reversing the order of integration $$\int\limits_0^2 {\int\limits_{{x^2}}^{2x} {f\left( {x,y} \right)dy\,dx} }$$ may... GATE ECE 1995 The function $$y = {x^2} + {{250} \over x}$$ at $$x=5$$ attains GATE ECE 1994 ## Marks 2 More Let r = x2 + y - z and z3 - xy + yz + y3 = 1. Assume that x and y are independent variables. At (x, y, z) = (2, -1, 1), ... GATE ECE 2018 A three dimensional region $$R$$ of finite volume is described by $$\,\,{x^2} + {y^2} \le {z^3},\,\,\,0 \le z \le 1$$ W... GATE ECE 2017 Set 1 Let $$\,\,f\left( x \right) = {e^{x + {x^2}}}\,\,$$ for real $$x.$$ From among the following. Choose the Taylor series a... GATE ECE 2017 Set 1 The minimum value of the function $$f\left( x \right) = {1 \over 3}x\left( {{x^2} - 3} \right)\,\,$$ in the interval $$... GATE ECE 2017 Set 2 The values of the integrals$$\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dy... GATE ECE 2017 Set 2 A triangle in the $$xy-$$plane is bounded by the straight lines $$2x=3y, y=0$$ and $$x=3.$$ The volume above the triangl... GATE ECE 2016 Set 3 The region specified by $$\left\{ {\left( {\rho ,\varphi ,{\rm Z}} \right):3 \le \rho \le 5,\,\,{\pi \over 8} \le \ph... GATE ECE 2016 Set 1 The integral$$\,\,{1 \over {2\pi }}\int {\int_D {\left( {x + y + 10} \right)dxdy\,\,} } $$where$$D$$denotes the disc... GATE ECE 2016 Set 1 The value of the integral$$\int_{ - \infty }^\infty {12\,\,\cos \left( {2\pi t} \right){{\sin \left( {4\pi t} \right)}... GATE ECE 2015 Set 2 Which one of the following graphs describes the function? $$f\left( x \right) = {e^{ - x}}\left( {{x^2} + x + 1} \right)... GATE ECE 2015 Set 1 The maximum area (in square units) of a rectangle whose vertices lie on the ellipse$${x^2} + 4{y^2} = 1\,\,$$is GATE ECE 2015 Set 1 The maximum value of$$f\left( x \right) = 2{x^3} - 9{x^2} + 12x - 3$$in the interval$$\,0 \le x \le 3$$is _________... GATE ECE 2014 Set 3 For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have m... GATE ECE 2014 Set 4 The volume under the surface$$z\left( {x,y} \right) = x + y$$and above the triangle in the$$xy$$plane defined by ... GATE ECE 2014 Set 1 The Taylor series expansion of$$3sinx+2cosx$$is GATE ECE 2014 Set 1 The Taylor series expansion of$$\,\,{{\sin x} \over {x - \pi }}\,\,$$at$$x = \pi $$is given by GATE ECE 2009 In the Taylor series expansion of$${e^x} + \sin x$$about the point$$x = \pi ,$$the coefficient of$${\left( {x = \p... GATE ECE 2008 The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line ... GATE ECE 2008 Consider the function $$\,f\left( x \right) = {x^2} - x - 2.\,$$ The maximum value of $$f(x)$$ in the closed interval $$... GATE ECE 2007$$\int\limits_0^{{\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2\$}}} {...
GATE ECE 2000

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