Recent questions tagged bookproblem

Differentiate the functions with respect to x: $\;2\sqrt {cot (x^2)}$

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Let $A$ and $B$be sets. Show that$f : A × B \to\; B×A$such that $ f(a,b)\,=\,(b,a)$ is bijective function

asked Nov 8, 2012 by vaishali.a

1 answer

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.(i) $f : R\; \to R\; defined \; by \; f(x)\; =\; 3-4x$

asked Nov 8, 2012 by vaishali.a

1 answer

Differentiate the functions with respect to x: $ cos \; x^3. sin^2 (x)^5 $

asked Nov 8, 2012 by thanvigandhi_1

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

Let $A=\{1,2,3\},\; B = \{4,5,6,7\}$ and let $f = \{(1,4),(2,5),(3,6)\}$be a function from $A$ to $B$. Show that $f$ is one-one.

asked Nov 8, 2012 by vaishali.a

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

Show that the Modulus Function $f : R \to R$, given by $ f(x) = |\;x\;|$, is neither one-one nor onto, where$ |\;x\;|\; is\; x$, if $x$ is positive or $0$ and $|\;x\;|\; is\; $ $-$$x$, if $ x$ is negative.

asked Nov 8, 2012 by vaishali.a

1 answer

Prove that the Greatest Integer Function $f : R \to R$, given by $f (x) = [x]$, is neither one-one nor onto, where $[x]$ denotes the greatest integer less than or equal to $x$.

asked Nov 8, 2012 by vaishali.a

1 answer

Check the injectivity and surjectivity of the function: $f : N\to N\; given\; by\; f(x)\; = x^2 $

asked Nov 8, 2012 by vaishali.a

1 answer

Show that the function $f : R_* \rightarrow R_* $ defined by $ f(x) = (\frac{1} {x})$ is one-one and onto, where $R_* $ is the set of all non-zero real numbers. Is the result true, if the domain $R_* $ is replaced by $N$ with co-domain being same as $R_*$?

asked Nov 8, 2012 by vaishali.a

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 each of the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $(i) R = \{(a,b) |a-b|$ is a multiple of 4 $\}$ is an equivalence relation. Find the set of all elements related to 1.

asked Nov 7, 2012 by vaishali.a

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

Differentiate the functions with respect to $x$: $sec \;( tan (\sqrt x ) )$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Differentiate the function with respect to x: $cos\;(sin x)$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Differentiate the functions with respect to x: $ \; sin ( x^2 + 5 ) $

asked Nov 7, 2012 by thanvigandhi_1

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

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below: \[\] \begin{array}{cccc} \textbf{Types} & \textbf{Machine I} & \textbf{Machine II}& \textbf{Machine III}\\ A&12&18&6 \\ B&6&0&9 \end{array} \[\] Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, Formulate the L.P.P and solve to find the maximum profit.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below: \[\]$\begin{array}{cccc} \textbf{Food} & \textbf{Vitamin A} & \textbf{Vitamin B}& \textbf{Vitamin C}\\ X & 1 & 2 &3 \\ Y & 2 & 2 &1 \end{array}$\[\] One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet?

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Read the details below and Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag? A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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