Recent questions tagged sec1

Find all points of discontinuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} |\;x\;| + 3,& \quad\text{ if $ x $ $\leq -3$}\\ -2x ,& \quad \text{if $-3$ <x< 3}\\ 6x+2, & \quad\text{if $x$ $\geq 3$}\\ \end{array} \right. $

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Let $R$ be the relation in the set $N$ given by $R=\{(a,b): a=b-2, b>6\}$. Choose the correct answer:

asked Nov 8, 2012 by vaishali.a

1 answer

Let $R$ be the relation in the set $\{1, 2, 3, 4\}$ given by $R = \{(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)\}$. Choose the correct answer.

asked Nov 8, 2012 by vaishali.a

1 answer

Let $L$ be the set of all lines in $XY$ plane and $R$ be the relation in $L$ defined as $R = \{(L1, L2) : L1\:$ is parallel to $L2\}$. Show that $R$ is an equivalence relation. Find the set of all lines related to the line $y = 2x + 4.$

asked Nov 8, 2012 by vaishali.a

1 answer

Show that the relation $R$ defined in the set $A$ of all polygons as $R = \{(P_1, P_2) :\: P_1\ and \;P_2$ have same number of sides$\}$, is an equivalence relation. What is the set of all elements in $A$ related to the right angle triangle $T$ with sides $3, 4$ and $5$?

asked Nov 8, 2012 by vaishali.a

1 answer

Show that the relation $R$ defined in the set $A$ of all triangles as $R = \{(T_1, T_2) : T_1\,is\, similar\, to\, T_2\}$, is equivalence relation. Consider three right angle triangles $(T_1 \;$ with sides $3, 4, 5, \; T_2$ with sides $5, 12, 13$, and $T_3$, with sides $6, 8, 10$) Which triangles among $T_1\, T_2\, and\, T_3$ are related?

asked Nov 8, 2012 by vaishali.a

1 answer

The relation $R$ in the set $A$ of points in a plane given by $R = \{(P, Q)$ : distance of the point $P$ from the origin is same as the distance of the point $Q$ from the origin $\}$, is

asked Nov 8, 2012 by vaishali.a

1 answer

Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} 2x + 3,& \quad\text{ if $ x $ $\leq 2$}\\ 2x - 3,& \quad \text{if $x$ > 1}\\ \end{array} \right. $

asked Nov 7, 2012 by thanvigandhi_1

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

Show that the relation $R$ in the set $A= \{1,2,3,4,5\} $given by $R = \{(a, b) : |a – b| \,is\, even \} $, is an equivalence relation. Show that all the elements of $\{1, 3, 5\} $ are related to each other and all the elements of $\{2, 4\}$ are related to each other. But no element of $ \{1, 3, 5 \} $ is related to any element of $\{2, 4\}$.

asked Nov 7, 2012 by vaishali.a

1 answer

Show that the relation $R$ in the set $A$ of all the books in a library of a college, given by ( $R = \{ (x, y) : x\;$ and $\; y\;$ have same number of pages$\}$ ) is an equivalence relation.

asked Nov 7, 2012 by vaishali.a

1 answer

Show that the relation $R$ in the set {1,2,3} given by R={(1,2), (2,1)} is symmetric but neither reflexive nor transitive.

asked Nov 7, 2012 by vaishali.a

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

Show that the relation $R$ in $R$ defined as $R = {(a, b) : a \leq b} $, is reflexive and  transitive but not symmetric.

asked Nov 7, 2012 by vaishali.a

1 answer

Check whether the relation R defined in the set ${1, 2, 3, 4, 5, 6}$ as $R= {(a,b) : b= a+1}$ is reflexive, symmetric or transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x . cos\; x \]

asked Nov 7, 2012 by thanvigandhi_1

0 answers

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x - cos\; x \]

asked Nov 7, 2012 by thanvigandhi_1

0 answers

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x + cos\; x \]

asked Nov 7, 2012 by thanvigandhi_1

0 answers

Show that the relation $R$ in the set $R$ of real numbers, defined as $(R) =\{(a, b: (a \leq b^2 )\}$ is neither reflexive nor symmetric nor transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

Examine the following functions for continuity. $f(x) = | \;x - 5\;|$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity $\; f(x) = \large \frac {x^2 - 25} {x + 5}$$, x\:\neq\: -5$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity. $f(x) = \frac {1} { x - 5}, x \: \neq \: 5 $

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity. $f(x) = x-5$

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Find all the points of discontinuity of $f$ defined by $f (x) = | x | – | x + 1 |.$

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Examine that sin | x | is a continuous function.

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Show that the function defined by f (x) = | cos x | is a continuous function.

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Show that the function defined by $ f (x) = cos (x^2) $ is a continuous function.

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Show that the function defined by $ g (x) = x – [x] $ is discontinuous at all integral points. Here $ [x] $ denotes the greatest integer less than or equal to $x$.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Is the function defined by $ f (x) = x^2 - \sin\; x + 5 $ continuous at $ x =\pi $ ?

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Prove that the function $ f (x) = x^n $ is continuous at $ x = n $, where n is a positive integer.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Examine the continuity of the function $f (x) = 2x^2 - 1$ at $x = 3$

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Prove that the function $f (x) = 5x-3$ is continuous at $x=0$, $x=-3$ and $x=5$.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Ask Questions, Get Answers

Find all points of discontinuity of \(f\), where \(f\) is defined by $ f(x) = \left\{ \begin{array} {1 1} |\;x\;| + 3,& \quad\text{ if $ x $ \(\leq -3\)}\\ -2x ,& \quad \text{if $-3$ <x< 3}\\ 6x+2, & \quad\text{if $x$ \(\geq 3\)}\\ \end{array} \right. $

Let $R$ be the relation in the set $N$ given by $R=\{(a,b): a=b-2, b>6\}$. Choose the correct answer:

Let $R$ be the relation in the set $\{1, 2, 3, 4\}$ given by $R = \{(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)\}$. Choose the correct answer.

Let \(L\) be the set of all lines in \(XY\) plane and \(R\) be the relation in \(L\) defined as \(R = \{(L1, L2) : L1\:\) is parallel to \(L2\}\). Show that \(R\) is an equivalence relation. Find the set of all lines related to the line \(y = 2x + 4.\)

Show that the relation \(R\) defined in the set \(A\) of all polygons as \(R = \{(P_1, P_2) :\: P_1\ and \;P_2\) have same number of sides\(\}\), is an equivalence relation. What is the set of all elements in \(A\) related to the right angle triangle \(T\) with sides \(3, 4\) and \(5\)?

The relation $R$ in the set $A$ of points in a plane given by $R = \{(P, Q)$ : distance of the point $P$ from the origin is same as the distance of the point $Q$ from the origin $\}$, is

Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} 2x + 3,& \quad\text{ if $ x $ \(\leq 2\)}\\ 2x - 3,& \quad \text{if $x$ > 1}\\ \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 $(x = 2)$?

Show that the relation \(R\) in the set \(A\) of all the books in a library of a college, given by ( $R = \{ (x, y) : x\;$ and $\; y\;$ have same number of pages$\}$ ) is an equivalence relation.

Show that the relation \(R\) in the set {1,2,3} given by R={(1,2), (2,1)} is symmetric but neither reflexive nor transitive.

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

Show that the relation \(R\) in \(R\) defined as \(R = {(a, b) : a \leq b} \), is reflexive and  transitive but not symmetric.

Check whether the relation R defined in the set ${1, 2, 3, 4, 5, 6}$ as $R= {(a,b) : b= a+1}$ is reflexive, symmetric or transitive.

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x . cos\; x \]

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x - cos\; x \]

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x + cos\; x \]

Show that the relation \(R\) in the set \(R\) of real numbers, defined as $(R) =\{(a, b: (a \leq b^2 )\}$ is neither reflexive nor symmetric nor transitive.

Examine the following functions for continuity. $f(x) = | \;x - 5\;|$

Examine the following functions for continuity $\; f(x) = \large \frac {x^2 - 25} {x + 5}$$, x\:\neq\: -5$

Examine the following functions for continuity. $f(x) = \frac {1} { x - 5}, x \: \neq \: 5 $

Examine the following functions for continuity. $f(x) = x-5$

Find all the points of discontinuity of $f$ defined by $f (x) = | x | – | x + 1 |.$

Examine that sin | x | is a continuous function.

Show that the function defined by f (x) = | cos x | is a continuous function.

Show that the function defined by \( f (x) = cos (x^2) \) is a continuous function.

Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

Show that the function defined by $ g (x) = x – [x] $ is discontinuous at all integral points. Here $ [x] $ denotes the greatest integer less than or equal to $x$.

Is the function defined by $ f (x) = x^2 - \sin\; x + 5 $ continuous at $ x =\pi $ ?

Prove that the function \( f (x) = x^n \) is continuous at \( x = n \), where n is a positive integer.

Examine the continuity of the function $f (x) = 2x^2 - 1$ at $x = 3$

Prove that the function $f (x) = 5x-3$ is continuous at $x=0$, $x=-3$ and $x=5$.