Recent questions tagged q6

$ \int \: \frac{\large x^3-x^2+x-1}{\large x-1}dx $

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Prove that the lines $x=py+q;z=ry+s$ and $x=p'y+q';z=r'y+s'$ are perpendicular if $pp'+rr'+1=0.$

asked Jan 3, 2013 by sreemathi.v

1 answer

A balloon which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the radius is 10 cm.

asked Jan 2, 2013 by thanvigandhi_1

0 answers

The radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate in which the area of the circle is increasing when the radius is 10 cm.

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Find whether f(x) is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\mid x\mid\cos\large\frac{1}{x}, \normalsize& if\;x\neq 0\\0, & if\;x=0\end{array}\right.$at x=0.

asked Dec 31, 2012 by sreemathi.v

1 answer

Write a value of $ \int \: \large\frac{dx}{\sqrt {4-x^2}} $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Evaluate : $\int \: 5^x dx $

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int\:\large \frac{dx}{\sqrt x + x} $

asked Dec 25, 2012 by thanvigandhi_1

0 answers

Using the properties of determinants, evaluate $\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

If \[ f(x) = \left\{ \begin{array}{l l} 1+x & \quad {when \: x\: \leq 2}\\ 5-x & \quad { when \: x\: \: \leq 3} \end{array} \right.\] , then \[ \begin{array} ((A)\: f\: is\: continuous \: at\: x = 2 \quad & (B)\: f\: is\: discontinuous \: at \: x = 2 \\(C) \: f\: is\: continuous\: at\: x = 3 \quad & (D)\: f\: is\: continuous\: at\: x = 3 \: and \: discontinuous \: at \: x=2 \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

0 answers

If possible,find the sum of the matrices A and B,where $A=\begin{bmatrix}\sqrt 3 & 1\\2 & 3\end{bmatrix},and\; B=\begin{bmatrix}x & y & z\\a & b &6\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Write the value of the following determinant : $ \begin {vmatrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end {vmatrix} $

asked Dec 21, 2012 by thanvigandhi_1

1 answer

Evaluate : $\int \mathrm \: \large\frac{x^2}{1+x^3} $$dx $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

If $f : R \rightarrow R$ is defined by $f(x)=x^2-3x+2$, write $f(f(x))$.

asked Dec 18, 2012 by sreemathi.v

1 answer

There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?

asked Dec 18, 2012 by thanvigandhi_1

1 answer

Find the equations of the planes that passes through three points. $(1, 1, -1), (6, 4, -5), (-4, -2, 3) $

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: \[ tan^{-1} \frac{1}{\sqrt{x^2 - 1}}, | x | > 1 \]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the values of x,y and z from the following equations:\[(i)\begin{bmatrix}4 & 3\\x & 5\end{bmatrix}=\begin{bmatrix}y & z\\1 & 5\end{bmatrix}\qquad(ii)\;\begin{bmatrix}x+y & z\\5+z & xy\end{bmatrix}=\begin{bmatrix}6 & 2\\5 & 8\end{bmatrix}\qquad(iii)\;\begin{bmatrix}x+y+z\\x+z\\y+z\end{bmatrix}=\begin{bmatrix}9\\5\\7\end{bmatrix}\]

asked Dec 7, 2012 by sreemathi.v

1 answer

Find the sum of the vectors $\overrightarrow a=\hat i − 2\hat j + \hat k, \overrightarrow b=−2\hat i + 4\hat j + 5\hat k$ and $\overrightarrow c = \hat i − 6\hat j – 7\hat k$ .

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the integral $\int(4\;e^{3x}+1)\;dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find $| \overrightarrow a |$ and $| \overrightarrow b |$ , if $(\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a − \overrightarrow b) = 8$ and $| \overrightarrow a |= 8 | \overrightarrow b |.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Integrate the function $\sqrt{ax+b}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function $\frac{(1+log\: x)^2}{x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\sin x\;\sin2x\;\sin3x$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x^2}{1-x^6}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{1-x^2}{x(1-2x)}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Given that $\overrightarrow a . \overrightarrow b = 0$ and $ \overrightarrow a$ x $\overrightarrow b = \overrightarrow 0$ What can you conclude about the vectors $\overrightarrow a$ and $ \overrightarrow b$?

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find a vector of magnitude $5$ units, and parallel to the resultant of the vectors $\overrightarrow a = 2\hat i + 3 \hat j - \hat k$ and $\overrightarrow b = \hat i - 2\hat j + \hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function\[x^2logx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in the smaller area enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is \[ \begin{array}{1} (A)\;2(\pi - 2) \qquad & (B)\;\pi - 2 \qquad &(C)\;2\pi - 1 \qquad & (D)\;2 ( \pi + 2) \end{array} \]

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area enclosed between the parabola $y^2 = 4ax$ and the line $y = mx.$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function $\sqrt{x^2+4x-5}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^4(x+e^{2x})dx$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_4^5e^x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region in the first quadrant enclosed by $x$ - axis, line $x = \sqrt {3}\: y$ and the circle $x^2 + y^2 = 4$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the integral using substitution\[\int\limits_0^2\frac{dx}{x+4-x^2}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_2^8\mid x-5 \mid\;dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{5x}{(x+1)(x^2+9)}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=x\sin x\qquad:xy'=y+x\sqrt{x^2-y^2} (x\neq0\;and\;x>y\;or\;x<-y)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles touching the $y$ - axis at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$=(1+x^2)(1+y^2)$

asked Nov 30, 2012 by sreemathi.v

1 answer

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+2y=x^2\log x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the cartesian equation of the line which passes through the point (-2, 4, -5) and parallel to the line given by $\frac{\large x+3}{\large 3} = \frac{\large y-4}{\large 5} = \frac{\large z+8}{\large 6}$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that \[ cos^{-1} \frac {12}{13} +sin^{-1} \frac{3}{5}=sin^{-1} \frac{56}{65}\]

asked Nov 29, 2012 by vaishali.a

1 answer

Prove that $ \begin{vmatrix} a^2&bc&ac+c^2\\ a^2+ab& b^2& ac\\ ab&b^2+bc&c^2 \end{vmatrix}=4\,a^2\;b^2\;c^2. $

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

Solve the following Linear Programming Problems graphically: Minimise $Z = x + 2y$, subject to $2x + y \geq 3, x + 2y \geq 6, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}\;$$=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} -1&5 \\ -3&2 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

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