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## Marks 1

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For the two functions $$f\left( {x,y} \right) = {x^3} - 3x{y^2}\,\,$$ and $$\,\,g\left( {x,y} \right) = 3{x^2}y - {y^3}... GATE PI 2016 At$$x=0,$$the function is$$f\left( x \right) = \left| {\sin {{2\pi x} \over L}} \right|\left( { - \infty &lt; x &lt;...
GATE PI 2016
The function $$f\left( x \right) = {x^2} = x + x + x + ....x$$ times, is defined
GATE PI 2015
At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has
GATE PI 2012
$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ is
GATE PI 2012
Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the po...
GATE PI 2012
The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is
GATE PI 2012
The total derivative of the function $$'xy'$$ is
GATE PI 2009
The value of the expansion $$\mathop {Lim}\limits_{x \to 0} \left[ {{{\sin \left( x \right)} \over {{e^x}X}}} \right]\,\... GATE PI 2008 The value of the integral$$\,\,\int\limits_{ - \pi /2}^{\pi /2} {\left( {x\,\cos \,x} \right)dx\,\,} $$is GATE PI 2008 What is the value of$$\mathop {Lim}\limits_{x \to \pi /4} {{\cos x - \sin x} \over {x - \pi /4}}\,\,$$GATE PI 2007 For the function$$\,\,f\left( {x,y} \right) = {x^2} - {y^2}\,\,$$defined on$${R^2},$$the point$$(0,0)$$is GATE PI 2007 Given$$y = \int\limits_1^{{x^2}} {\cos t\,\,\,dt,} {\,\,\,}$$then$${{dy} \over {dx}} = \_\_\_\_\_.$$GATE PI 1995 ## Marks 2 More$$\mathop {\lim }\limits_{x \to 0} \left( {{{{e^{5x}} - 1} \over x}} \right)$$is equal to ________. GATE PI 2016 The range of values of$$k$$for which the function$$\,\,f\left( x \right) = \left( {{k^2} - 4} \right){x^2} + 6{x^3} +...
GATE PI 2016
The curve $$\,\,y = {x^4}\,\,$$
GATE PI 2015
The value of $$\mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} {{{x^2} - xy} \over {\sqrt x - ... GATE PI 2015 A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profil... GATE PI 2012 The integral$$\,\,{1 \over {\sqrt {2\pi } }}\int\limits_{ - \infty }^\infty {{e^{{{ - {x^2}} \over 2}}}} dx\,\,$$is e... GATE PI 2010 If$$f\left( x \right) = \sin \left| x \right|\,\,$$then the value of$${{df} \over {dx}}\,\,$$at$$\,\,x = {{ - \pi }...
GATE PI 2010

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