Recent questions tagged q5

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: $\: f (x) = x^3, x \in [– 2, 2] $

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1\%$.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$

asked Nov 25, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Find the slope of the normal to the curve $ x = a \cos^3\theta, \: y = a \sin^3\theta$ at $ \theta =\Large {\frac{\pi}{4}}$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the matrix $B'AB$ is symmetric or skew symmetric according as A is symmetric or skew symmetric.

asked Nov 23, 2012 by pady_1

1 answer

Find the intervals in which the function f given by $f (x) = 2x^3 – 3x^2 – 36 x + 7$ is (a) strictly increasing and (b) strictly decreasing ?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A stone is dropped into a quiet lake and waves move in circles at the speed of $5 \;cm/s$. At the instant when the radius of the circular wave is $8 \;cm$, how fast is the enclosed area increasing?

asked Nov 22, 2012 by thanvigandhi_1

1 answer

Show that the function $f : R \to R$ given by $f (x) = x^3$ is injective.

asked Nov 21, 2012 by vaishali.a

1 answer

Let $\ast '$ be the binary operation on the set $\{1, 2, 3, 4, 5\}$ defined by $a \ast ' b = H.C.F$ of a and b. Is the operation same as the operation $\ast$ defined in the table below? $\begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}$

asked Nov 21, 2012 by vaishali.a

1 answer

Differentiate w.r.t. $x$ the function in $\large\frac{\cos^{ -1}\Large\frac{ x}{ 2}}{\sqrt {2x + 7}}, \normalsize-2 < x < 2 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Verify Mean Value Theorem, if $ f (x) = x^3 - 5x^2 - 3x $ in the interval $ [a,b]$, where $ a = 1$ and $ b = 3$. Find all $ c \in (1,3) $ for which $ f'(c) = 0$.

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^3 \log x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = \cos \theta -\ cos 2\theta, y = \sin \theta -\ sin 2\theta $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x + 3)^2 \: . \: (x + 4)^3 \: . \: (x + 5)^4 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : \log\;( cos \: e^x ) $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.

asked Nov 16, 2012 by fingeazy

1 answer

An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?

asked Nov 15, 2012 by fingeazy

1 answer

Find $ \frac {dy}{dx} $ in the following: $ x^2 +xy + y^2 = 100 $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

State with reason whether following functions have inverse: (iii) $h: \{2,3,4,5,\} \to \{7,9,11,13\}$ with $h=\{(2,7),(3,9),(4,11),(5,13) \} $

asked Nov 9, 2012 by vaishali.a

1 answer

Differentiate the functions with respect to $x: \large \frac{ sin\; (ax + b) } { cos \;( cx + d)} $

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Show that the Signum Function $f : R \to R$, given by \[ f(x) = \left\{ \begin{array}{l l} 1, & if \; x \; > 0 \\ 0, & if\; x\;= 0 \text{ is neither one-one nor onto } \\ -1, & if\; x \;< 0 \end{array} \right. \]

asked Nov 8, 2012 by vaishali.a

1 answer

Is the function f defined by $f(x) = \left\{\begin{array}{l l} x, & \quad \text{if $x$ $ \leq $ 1}\\ 5, & \quad \text{if $x$ > 1}\\ \end{array} \right.$ continuous at $(x = 0)$? At $(x = 1)$? At $(x = 2)$?

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Check whether the relation $R$ in $R$ defined by $R = {(a, b) : a \leq b^3}$ is reflexive, symmetric or transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

If the coordinates of the points $A, B, C, D$ be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then find the angle between the lines $AB$ and $CD$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Ask Questions, Get Answers

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: $\: f (x) = x^3, x \in [– 2, 2] $

Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1\%$.

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix} $

Find the slope of the normal to the curve $ x = a \cos^3\theta, \: y = a \sin^3\theta$ at $ \theta =\Large {\frac{\pi}{4}}$.

Show that the matrix $B'AB$ is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Find the intervals in which the function f given by $f (x) = 2x^3 – 3x^2 – 36 x + 7$ is (a) strictly increasing and (b) strictly decreasing ?

A stone is dropped into a quiet lake and waves move in circles at the speed of $5 \;cm/s$. At the instant when the radius of the circular wave is $8 \;cm$, how fast is the enclosed area increasing?

Show that the function \(f : R \to R\) given by \(f (x) = x^3\) is injective.

Differentiate w.r.t. \(x\) the function in \(\large\frac{\cos^{ -1}\Large\frac{ x}{ 2}}{\sqrt {2x + 7}}, \normalsize-2 < x < 2 \)

Verify Mean Value Theorem, if \( f (x) = x^3 - 5x^2 - 3x \) in the interval \( [a,b]\), where \( a = 1\) and \( b = 3\). Find all \( c \in (1,3) \) for which \( f'(c) = 0\).

Find the second order derivatives of the functions given in $ x^3 \log x $

If $x$ and $y$ are connected parametrically by the equations given in $ x = \cos \theta -\ cos 2\theta, y = \sin \theta -\ sin 2\theta $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

Differentiate the functions given in w.r.t. $x : $ $ (x + 3)^2 \: . \: (x + 4)^3 \: . \: (x + 5)^4 $

Differentiate the following w.r.t. $x : \log\;( cos \: e^x ) $

Find $ \frac {dy}{dx} $ in the following: $ x^2 +xy + y^2 = 100 $

State with reason whether following functions have inverse: (iii) \(h: \{2,3,4,5,\} \to \{7,9,11,13\}\) with \(h=\{(2,7),(3,9),(4,11),(5,13) \} \)

Differentiate the functions with respect to $x: \large \frac{ sin\; (ax + b) } { cos \;( cx + d)} $

Show that the Signum Function \(f : R \to R\), given by \[ f(x) = \left\{ \begin{array}{l l} 1, & if \; x \; > 0 \\ 0, & if\; x\;= 0 \text{ is neither one-one nor onto } \\ -1, & if\; x \;< 0 \end{array} \right. \]

Is the function f defined by $f(x) = \left\{\begin{array}{l l} x, & \quad \text{if $x$ \( \leq \) 1}\\ 5, & \quad \text{if $x$ > 1}\\ \end{array} \right.$ continuous at $(x = 0)$? At $(x = 1)$? At $(x = 2)$?

Check whether the relation $R$ in $R$ defined by $R = {(a, b) : a \leq b^3}$ is reflexive, symmetric or transitive.

If the coordinates of the points $A, B, C, D$ be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then find the angle between the lines $AB$ and $CD$.