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Recent questions tagged p136

Show that $f(x)=2x+\cot^{-1}x+log\bigg(\sqrt {(1+x^2)}-x\bigg)$ is increasing in R.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that the line $\Large \frac{x}{a}+\frac{y}{b}\normalsize=1$,touches the curve $y=b.e^{\Large \frac{-x}{a}}$ at the point where the curve intersects the axis of y.

asked Jan 11, 2013 by sreemathi.v

1 answer

At what points on the curve $x^2+y^2-2x+4y+1=0$,the tangents are parallel to the y-axis?

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the equation of the normal lines to the curve $3x^2-y^2=8$ which are parallel to the line x+3y=4.

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that the curves $y^2=4x$ and $x^2+y^2-6x+1=0$ touch each other at the point (1,2).

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the angle of intersection of the curves $y=4-x^2$ and $y=x^2$.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the co-ordinates of the point on the curve $\sqrt x\quad \sqrt y=4$ at which tangent is equally inclined to the axes.

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that the curves $xy=4$ and $x^2+y^2=8$ touch each other.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the condition that the curves $2x=y^2$ and $2xy=k$ intersect orthogonally.

asked Jan 11, 2013 by sreemathi.v

1 answer

x and y are the sides of two squares such that $y=x-x^2$.Find the rate of change of the area of second square with respect to the area of first square.

asked Jan 11, 2013 by sreemathi.v

1 answer

The volume of a cube increases at a constant rate.Prove that the increase in its surface area varies inversely as the length of the side.

asked Jan 11, 2013 by sreemathi.v

1 answer

A swimming pool is to be drained for cleaning .If L represents the number of litres of water in the pool seconds after the pool has been plugged off to drain and $L=200(10-t)^2$.How fast is the water running out at the end of 5 seconds?What is the average rate at which the water flows out during the first 5 seconds?

asked Jan 11, 2013 by sreemathi.v

1 answer

Solve system of linear equations, using matrix method:\[\] \[x-y+2z=7\] \[3x+4y-5z=-5\] \[2x-y+3z=12\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[2x+3y+3z=5\] \[x-2y+z=-4\] \[3x-y-2z=3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[x-y+z=4\] \[2x+y-3z=0\] \[x+y+z=2\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[2x+y+z=1\] \[x-2y-z = \frac{3}{2}\] \[3y-5z=9\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:<br>$5x+2y=3$ <br> $3x+2y=5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:<br>$4x-3y=3$ <br> $3x-5y=7$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:<br> $2x-y=-2$ <br> $3x+4y = 3$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: <br>$5x+2y=4 $<br>$7x+3y = 5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 5x -y +4z = 5 \] \[\quad2x + 3y + 5z= 2\] \[\quad 5x - 2y + 6z = -1\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 3x -y -2z = 2 \] \[\quad 2y -z = -1\] \[\quad 3x -5y = 3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + y + z = 1 \] \[\quad 2x + 3y +2z = 2\] \[\quad ax + ay +2az = 4\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + 3y = 5 \] \[\quad 2x + 6y = 8\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 2x -y = 5 \] \[\quad x + y = 4\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + 2y = 2 \] \[\quad 2x + 3y = 3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

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