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GATE PI

Calculus

Engineering Mathematics

Previous Years Questions

Marks 1

More
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 < x <...
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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