Recent questions tagged q5

Answer the following as true or false. $\\(i)\; \overrightarrow a$ and -$\overrightarrow a$ are collinear.

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Find the scalar and vector components of the vector with initial point $(2, 1)$ and terminal point $(– 5, 7).$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find an anti derivative(or integral)of the function by the method of inspection $\sin2x-4e^{3x}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Show that each of the given three vectors is a unit vector: $ \large\frac{1}{7}$$ ( 2\hat i + 3\hat j + 6\hat k),\large\frac{1}{7}$$ ( 3\hat i - 6\hat j + 2\hat k), \large\frac{1}{7}$$ ( 6\hat i + 2\hat j - 3\hat k) $ Also, show that they are mutually perpendicular to each other.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Integrate the function $\sin(ax+b)\;\cos(ax+b)$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^3x\;\cos^3x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{3x}{1+2x^4}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions $\frac{2x}{x^2+3x+2}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find $λ$ and $μ$ if $ ( 2\hat i + 6\hat j + 27\hat k)\times (\hat i + λ\hat j + μ\hat k) = \overrightarrow 0$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the value of $x$ for which $x(\hat i + \hat j +\hat k)$ is a unit vector.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function $x\; \log2x $

asked Dec 4, 2012 by sreemathi.v

1 answer

Using integration find the area of the triangular region whose sides have the equations $y = 2x + 1, y = 3x + 1$ and $x = 4.$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area bounded by the curve $(y = \sin\; x) $ between $ (x = 0) $ and $(x = 2π).$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function $\sqrt{1-4x-x^2}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums\[\int\limits_{-1}^1e^xdx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 2}\cos 2x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 4 } + \frac{\Large y^2}{\Large 9} = 1$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the integral using substitution\[\int\limits_0^\frac{\large \pi}{2}\frac{\sin x}{1+\cos^2x}dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_{-5}^5\mid x+2 \mid\;dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}\qquad[Hint:\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}=\frac{1}{x^\frac{1}{3}\bigg(1+x^\frac{1}{6}\bigg)},put\;x=t^6]\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=Ax\qquad:\;xy'\;=\;y\;(x\neq0)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^x(a\;\cos x+b\;\sin x)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $(e^x+e^{-x})\;dy-(e^x-e^{-x})\;dx=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x^2\large\frac{dy}{dx}$$=x^2-2y^2+xy$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $\cos^2x\large\frac{dy}{dx}$$+y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the equation of the line in vector and in cartesian form that passes through the point with position vector $2\hat{ i}- \hat{j} + 4\hat{k}$ and is in the direction$\hat{i} + 2\hat{j} - \hat{k}$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the direction cosines of the sides of the triangle whose vertices are (3, 5, -4), (-1, 1, 2) and ( -5, -5, -2).

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that \[cos^{-1} \frac {4}{5} +cos^{-1} \frac{12}{13}=cos^{-1} \frac{33}{65}\]

asked Nov 29, 2012 by vaishali.a

1 answer

Solve the equation $ \begin{vmatrix} x+a & x & x \\ x & x+a & x\\ x & x & x+a \end{vmatrix}=0, \; a \neq 0. $

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

Solve the following Linear Programming Problems graphically: Maximise $Z = 3x + 2y$ subject to $x + 2y \leq 10, 3x + y \leq 15, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2&-2 \\ 4&3 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If $\Delta = \begin{vmatrix} a_11&a_12&a_13 \\ a_21&a_22&a_23 \\ a_31&a_32&a_33 \end{vmatrix} $ and $A_y$ is Cofactor of $a_y$, then value of $\Delta$ is:

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If area of triangle is $35\; sq\; units$ with vertices $(2, -6), (5, 4)$ and $(k, 4)$. Then $k$ is

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} b+c&q+r&y+z \\ c+a&r+p&z+x \\ a+b&p+q&x+y \end{vmatrix} = 2 \begin{vmatrix} a&p&x \\ b&q&y \\ c&r&z \end{vmatrix} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Evaluate the determinant: $\begin{vmatrix} 3&-1&-2 \\ 0&0&-1 \\3&-5&0 \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the principal values of the following: $cos^{-1} \bigg(-\frac {1} {2} \bigg ) $

asked Nov 28, 2012 by vaishali.a

2 answers

Determine order and degree (if defined) of differential equation $\frac{d^2y}{dx^2}=\cos3x+\sin3x$

asked Nov 28, 2012 by sreemathi.v

1 answer