Recent questions tagged 2012

$ \int \: \large\frac{x^3+5x^2-4}{x^2}\normalsize dx. $

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Find the value of the parallelopipped whose edges are $ \overrightarrow a = 2\hat i - 3\hat j + 4\hat k, \overrightarrow b = \hat i - 2\hat j - \hat k \: and \: \overrightarrow c = 2\hat i - \hat j + 2\hat k $

asked Jan 2, 2013 by thanvigandhi_1

0 answers

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

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Write the direction cosines of a line equally inclined to the three coordinate axes.

asked Jan 2, 2013 by thanvigandhi_1

0 answers

(i) Is the binary operation * defined on set N, given a * b = $ \large\frac{a+b}{2} $ for all a, b $ \in$ N, comutative? (ii) Is the above binary operation * associative ?

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Write the following functions in the simplest form : \[ (i) tan^{-1} \bigg( \frac{\sqrt{1+x^2} - 1}{x} \bigg), x \neq 0 \] \[(ii) tan^{-1} \frac{1}{\sqrt{x^2-1}} ,| x | > 1 \]

asked Dec 31, 2012 by thanvigandhi_1

1 answer

Using properties of determinants, prove the following: $ \begin{bmatrix} a^2+1 \quad & ab \quad & ac \\ ab \quad & b^2+1 \quad & bc \\ ca \quad & cb \quad & c^2+1 \end{bmatrix} = 1+a^2+b^2+c^2. $

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Prove that : $ (i) \large \frac{d}{dx} $$(a^x) = a^x log_e a. \; (ii) \large\frac{d}{dx}$$ (e^x) = e^x. $

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Find all the points of discontinuity of f, where $ f(x) = \left \{ \begin{array}{1 1} \large\frac{sinx}{x}, \quad & if\: x < 0 \\ x+1, \quad & if\: x \geq 0 \end{array}\right \}. $

asked Dec 31, 2012 by thanvigandhi_1

0 answers

A point source of light along a straight road is a height of 'a' metres. A boy 'b' metres in height is walking along the road. How fast is his shadow increasing if he is walking away from the light at the rate of c metres per minute.?

asked Dec 31, 2012 by thanvigandhi_1

0 answers

The two equal sides of an isosceles triangles with fixed base b cm are decreasing at the rate of 3 cm/sec. How fast is the area decreasing when two equal sides are equal to the base.

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int \: \bigg[ \large\frac{1}{log \: x} - \large\frac{1}{(log\: x )^2} \bigg]$$ dx. $

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Integrate : $\int \:\large \frac{x}{(x-1)^2(x+2)} $

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Integrate : $ \int \: \large\frac{3x+5}{x^2-x^2-x-1} $

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Integrate : $\int \: x(\ log x )^2dx.$

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Show that four points with position vectors $ 6\hat i - 7\hat j, 19 \hat j - 4\hat k, 3\hat j - 6\hat k \: and \: 2\hat i + 5\hat j + 10\hat k$ are not co-planar.

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Find the equation of the plane passing through the points ( 1, 2, 3 ) and (0, -1, 0 ) and parrallel to the line, $ \large\frac{x-1}{2} = \frac{y+2}{3} = \frac{z}{-3} $.

asked Dec 31, 2012 by thanvigandhi_1

1 answer

Find the image of the point ( 1, 2, 3 ) in the plane $ x + 2y + 4z = 38$.

asked Dec 31, 2012 by thanvigandhi_1

0 answers