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Recent questions tagged easy

Integrate the functions\[\frac{x^2}{\sqrt{x^6+a^6}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{\sec^2x}{\sqrt{\tan^2x+4}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

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

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{9x^2+6x+5}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{7-6x-x^2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

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

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{8+3x-x^2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions $\frac{1}{\sqrt{(x-a)(x-b)}}$

asked Dec 5, 2012 by sreemathi.v

1 answer

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

asked Dec 5, 2012 by sreemathi.v

1 answer

Choose the correct answer in $\Large \int \normalsize\frac{\large dx}{\large x^2+2x+2}$ equals

asked Dec 5, 2012 by sreemathi.v

1 answer

$\Large \int \normalsize\frac{dx}{\sqrt{9x-4x^2}}$ equals

asked Dec 5, 2012 by sreemathi.v

1 answer

Find a unit vector perpendicular to each of the vector \( \overrightarrow a + \overrightarrow b\) and \( \overrightarrow a - \overrightarrow b\), where \( \overrightarrow a = 3\hat i + 2\hat j + 2\hat k\) and \( \overrightarrow b = \hat i + 2\hat j - 2\hat k\)

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If a unit vector \(\overrightarrow a\) makes angles \( \frac{\large \pi}{\large 3} \) with \( \hat i, \frac{\large \pi}{\large 3} \) with \( \hat j\) and an acute angle \(θ\) with \( \hat k\) , then find \( θ \) and hence, the components of \( \overrightarrow a \) .

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that $ ( \overrightarrow a - \overrightarrow b) \times ( \overrightarrow a + \overrightarrow b) = 2 ( \overrightarrow a \times \overrightarrow b) $

asked Dec 5, 2012 by thanvigandhi_1

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

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

If either $ \overrightarrow a = \overrightarrow 0 $ or $ \overrightarrow b = \overrightarrow 0 $ then $ \overrightarrow a × \overrightarrow b = \overrightarrow 0$. Is the converse true? Justify your answer with an example.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the area of the triangle with vertices $A(1, 1, 2), B(2, 3, 5)$ and $C(1, 5, 5)$.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the area of the parallelogram whose adjacent sides are determined by the vectors $ \overrightarrow a = \hat i - \hat j + 3\hat k$ and $\overrightarrow b = 2\hat i - 7 \hat j + \hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Let the vectors $ \overrightarrow a$ and $ \overrightarrow b$ be such that $| \overrightarrow a | = 3$ and $ |\overrightarrow b | = \frac{\large \sqrt 2}{\large 3}$ , then $\overrightarrow a \times \overrightarrow b$ is a unit vector, if the angle between $ \overrightarrow a$ and $ \overrightarrow b$ is

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Write down a unit vector in XY plane, making an angle of 30 degress with the positive direction of $x$ axis.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the scalar components and magnitude of the vector joining the points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = \overrightarrow b + \overrightarrow c$, then is it true that $| \overrightarrow a | = | \overrightarrow b | + | \overrightarrow c |$? Justify your answer.

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

If $\overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - \hat j + 3\hat k$ and $\overrightarrow c = \hat i - 2\hat j + \hat k$, find a unit vector parallel to the vector $2\overrightarrow a - \overrightarrow b + 3\overrightarrow c$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

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

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \((2\overrightarrow a + \overrightarrow b)\) and \((\overrightarrow a - 3\overrightarrow b)\) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $ \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3} $

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Prove that \( (\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a + \overrightarrow b) =| \overrightarrow a |^2 + |\overrightarrow b |^2\), if and only if \(\overrightarrow a,\: \overrightarrow b\) are perpendicular, given \(\overrightarrow a ≠ 0, \overrightarrow b ≠ 0\).

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the following : let \( \overrightarrow a\) and \( \overrightarrow b\) be two unit vectors and θ is the angle between them. Then \( \overrightarrow a\ + \overrightarrow b\) is a unit vector if

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer if the value of $ \hat i.( \hat j\times \hat k)+ \hat j . (\hat i \times \hat k) +\hat k. (\hat i \times \hat j)$ is

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer if θ is the angle between any two vectors $\overrightarrow a$ and $\overrightarrow b$, then $| \overrightarrow a ⋅\overrightarrow b | \: = \: | \overrightarrow a \times\overrightarrow b |$ when θ is equal to

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If \(y = \begin{vmatrix} f(x) & g(x) & h(x) \\l & m &n \\ a & b & c \end{vmatrix}\), prove that \(\large\frac{dy}{dx}\normalsize = \begin{vmatrix} f'(x) & g'(x) & h'(x) \\l & m &n \\ a & b & c \end{vmatrix}\)

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using the fact that \(\sin (A + B) = \sin A \cos B + \cos A \sin B\) and the differentiation, obtain the sum formula for cosines.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If \(f (x) = |\; x\; |^3\), show that \(f ″(x)\) exists for all real \(x\) and find it.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function $\;\int\;x\;sin\;x$

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function\[x^2logx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function\[x\;\sec^2x\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function $\;\int\;(x^2+1)\;log\;x$

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function\[e^x(\sin x+\cos x)\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function $\;\int\;\frac{xe^x}{(1+x)^2}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the function $e^x \large($$ \large \frac{1}{x}$$-\large\frac{1}{x^2})$

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region bounded by the curves \(y = x^2 + 2, y = x, \: x = 0\) and \(x = 3.\)

asked Dec 4, 2012 by thanvigandhi_1

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

Choose the correct answer in $\Large \int \normalsize x^2e^{x^3}\;dx $ equals

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in $\int e^x\sec x(1+\tan x)\;dx$ equals

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area under the given curves and given lines: $ (i) \: y = x^2, x = 1, x = 2 \: and\: x - axis$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area between the curves \(y = x\) and \(y = x^2.\)

asked Dec 4, 2012 by thanvigandhi_1

2 answers

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

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