Recent questions tagged q8

Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function $\;\int\;x\;\tan^{-x}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the smaller region bounded by the ellipse $ \frac{\large x^2}{\large 9} + \frac{\large y^2}{\large 4} =1$ and the line $ \frac{\large x}{\large 3}+ \frac{\large y}{\large 2}= 1$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function $\sqrt{x^2+3x}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_\frac{\Large \pi}{\Large 6}^\frac{\Large \pi}{\Large 4}cosec x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

The area between $x = y^2$ and $x = 4$ is divided into two equal parts by the line $x = a$, find the value of $a$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the integral using substitution $\displaystyle\int\limits_1^2\bigg(\frac{1}{x}-\frac{1}{2x^2}\bigg)e^{2x}dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $ \begin{align}\int\limits_0^\frac{\pi}{4} log (1+\tan x)\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\begin{align}\frac{e^{5logx}-e^{4logx}}{e^{3logx}-e^{2logx}}\end{align}$

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 $y-\cos y=x\qquad:\;(y\sin y+\cos y+x)y'=y$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of ellipses having foci on $y$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $x^5\large\frac{dy}{dx}$$=-y^5$

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x\large\frac{dy}{dx}$$-y+x\sin\bigg(\large\frac{y}{x}\bigg)=$$0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(1+x^2)dy+2xy\;dx=\cot x\;dx\;(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the vector and the cartesian equations of the lines that passes through the origin and $(5, -2, 3).$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the equation of the plane passing through (a, b, c) and parallel to the plane $\hat{r}. (\hat{i}+\hat{j}+\hat{k}) = 2$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that \[tan^{-1} \frac{1}{5}+ tan^{-1} \frac{1}{7}+tan^{-1}\frac{1}{3}+tan^{-1} \frac{1}{8}= \frac{\pi}{4}\]

asked Nov 29, 2012 by vaishali.a

1 answer

Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(i)\ \; \left [adj A \right ]^{-1} = adj(A^{-1}) \;\;\;\; $

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

Show that the minimum of Z occurs at more than two points. Minimise and Maximise $Z = x + 2y$ subject to $ x + 2y \geq 100, 2x – y \leq 0, 2x + y \leq 200; x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1 \\ \end{bmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the equation of the curve passing through the point$\bigg(0,\large\frac{\pi}{4}\bigg)$ whose differential equation is $\sin x\cos y\;dx+\cos x\sin y\;dy\;=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $y'+y=e^x$

asked Nov 28, 2012 by sreemathi.v

1 answer

By using the properties of determinants show that $ (i) \quad \begin{vmatrix} 1&a&a^2 \\ 1&b&b^2 \\ 1&c&c^2 \end{vmatrix} = (a-b)(b-c)(c-a) $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

$ \text{If } \begin{vmatrix} x&2 \\ 18&x \end{vmatrix} = \begin{vmatrix} 6&2 \\ 18&6 \end{vmatrix}$, then $x$ is equal to:

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the principal values of the following : $\cot^{-1} (\sqrt 3) $

asked Nov 28, 2012 by vaishali.a

2 answers