Recent questions tagged bookproblem

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & 10 \\ 2 & 7 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 4 & 5 \\ 3 & 4 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

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Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} $

asked Nov 23, 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

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & 3 \\ 2 & 7 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

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

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

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Matrices $A$ and $B$ will be inverse of each other only if

asked Nov 23, 2012 by pady_1

1 answer

Let $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} $, show that $ (aI + bA)^n = a^nI + na^{n-1}bA $, where $\;I\;$ is the identity matrix of order 2 and $n \in N$.

asked Nov 23, 2012 by pady_1

1 answer

Find the equation of all lines having slope $0$ that are tangents to the curve $ y=\large \frac{1}{x^2-2x+3}$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the equation of all lines having slope $2$ that are tangents to the curve $ y= \large\frac{1}{x-3}, $$\: x \neq 3$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the equation of all lines having slope $–1$ that are tangents to the curve $ y= \large\frac{1}{x-1}, $$ \: x \neq 1$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the point on the curve $y = x^3 - 11x + 5$ at which the tangent is $y = x -11$.

asked Nov 23, 2012 by thanvigandhi_1

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Find a point on the curve $y = (x – 2)^2 $ at which the tangent is parallel to the chord joining the points $(2, 0)$ and $(4, 4)$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find points at which the tangent to the curve $y = x^3 - 3x^2 - 9x + 7$ is parallel to the $x$ - axis.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the normal to the curve $ x = 1 - a \sin\theta, y = b \cos^2\theta$ at $ \theta = \Large {\frac{\pi}{2}}$

asked Nov 23, 2012 by thanvigandhi_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

if $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$ prove that $A^n = \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix} , n \in N$.

asked Nov 23, 2012 by pady_1

1 answer

Find the slope of the tangent to the curve $y = x^3 - 3x + 2$ at the point whose $x$ - coordinate is $3$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the tangent to curve $ y = x^3 - x + 1$ at the point whose $x$ - coordinate is $2$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the tangent to the curve $\normalsize y =\large { \frac{x-1}{x-2},} \normalsize x \neq 2\; at\;x = 10$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the slope of the tangent to the curve $y = 3x^4 – 4x \; at\; x = 4.$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$ then prove that $ A^n = \begin{bmatrix} 1+2n & -4n \\ n & 1 - 2n \end{bmatrix} $ , where $n$ is any positive integer.

asked Nov 23, 2012 by pady_1

1 answer

The interval in which $y = x^2 e ^{- x}$ is increasing is

asked Nov 23, 2012 by thanvigandhi_1

1 answer

If $A$ and $B$ are symmetric matrices, prove that $AB - BA$ is a skew symmetric matrix.

asked Nov 23, 2012 by pady_1

1 answer

Prove that the function given by $f (x) = x^3 – 3x^2 + 3x - 100$ is increasing in $R.$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that the function $f$ given by $f (x) = \log \cos\: x$ is strictly decreasing on $ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly increasing on, $\left( \large {\frac{\pi}{2},} \normalsize \pi\right)$

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

Prove that the function $f$ given by $f (x) = \log \sin x$ is strictly increasing on$ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly decreasing on $\left( \large {\frac{\pi}{2}}, \pi\right)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the values of $x, y, z $ if the matrix $ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} $ satisfy the equation $A'A = I $

asked Nov 23, 2012 by pady_1

1 answer

Let $I$ be any interval disjoint from $[–1, 1]$. Prove that the function $f$ given by $ f(x) = x + \frac{1}{\large x}$ is strictly increasing on $I$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the least value of a such that the function $f$ given by $f (x) = x^2 + ax + 1$ is strictly increasing on $(1, 2).$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

On which of the following intervals is the function $f $ given by $f (x) = x^{100} + sin x –1$ strictly decreasing ?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

For what values of $x$,
$\begin{bmatrix} 1 & 2 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0 \\ 2 \\ x \end{bmatrix}$ = 0 ?

asked Nov 23, 2012 by pady_1

1 answer

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} $ show that $A^2 - 5A + 7I = 0$

asked Nov 23, 2012 by pady_1

1 answer

Find $x$, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} = 0 $

asked Nov 23, 2012 by pady_1

1 answer

Which of the following functions are strictly decreasing on $\left(0, \: \large {\frac{\pi}{2}}\right)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that the function $f$ given by $f (x) = x^2 – x + 1$ is neither strictly increasing nor strictly decreasing on $(– 1, 1).$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that the logarithmic function is strictly increasing on $(0, \infty).$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that $ y =\large { \frac{4\sin\theta}{(2+\cos\theta)}}-\normalsize \theta$ is an increasing function of $\theta$ in $\left[0, \: \large {\frac{\pi}{2}}\right]$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the values of $x$ for which $y = [x(x – 2)]^2$ is an increasing function.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that $ y = log(1+x)-\large {\frac{2x}{2+x}}, \normalsize x > – \normalsize 1$, is an increasing function of $x$ throughout its domain.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the intervals in which the following functions are strictly increasing or decreasing: $(a) \;x^2 + 2x - 5$

asked Nov 23, 2012 by thanvigandhi_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

Find the intervals in which the function $f$ given by $f (x) = 2x^2 - 3x$ is $(a) $ strictly increasing

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by $f (x) = \sin x$ is neither increasing nor decreasing in $(0, \pi)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by $f (x) = \sin x$ is strictly decreasing in $(\large {\frac{\pi}{2}},$$ \pi)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by $f (x) = \sin \;x$ is strictly increasing in $\left(0, \: \large {\frac{\pi}{2}}\right)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

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