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Recent questions tagged p12

Each of the following defines a relation on $N : (iii)\quad x\;y\;is\;square\; of\; an\; integer\;x,y\quad N$

asked Mar 4, 2013 by meena.p

1 answer

Each of the following defines a relation on $ N : (ii)\quad x+y=10,x,y\quad N$

asked Mar 4, 2013 by meena.p

1 answer

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$ (iv)\quad k(x)\;=\;x^2$

asked Mar 4, 2013 by meena.p

1 answer

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective$(iii)\quad h(x)\;=\;x|x| $

asked Mar 4, 2013 by meena.p

1 answer

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$(ii)\quad g(x)\;=\;|\;x\;|$

asked Mar 4, 2013 by meena.p

1 answer

Discuss the continuity of the following function at x = 0 $f(x)= \left\{ \begin{array}{1 1} \Large\frac{x^4+x^3+2x^2}{\tan ^{-1}x} & \quad ,\;x\neq0 \\ 10 & \quad ,\;x=0 \end{array} \right. $

asked Jan 25, 2013 by meena.p

1 answer

Let $ f(x)= \left\{ \begin{array}{1 1} |x|\cos \frac{1}{x} & \quad if\;x\neq0 \\ 0 & \quad if\;x=0 \end{array} \right. $ then discuss the continuity of f(x) at x = 0

asked Jan 25, 2013 by meena.p

1 answer

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

asked Jan 25, 2013 by meena.p

1 answer

The function $ \Large\frac{log(1+ax)-log(1-bx)}{x}$ is not defined at x = 0. Find the value of f(x) so that f(x) is continuous at x = 0.

asked Jan 25, 2013 by meena.p

1 answer

Show that the function $f(x) = | \sin x+\cos x| $ is continuous at $ x =\Large\pi$

asked Jan 25, 2013 by meena.p

1 answer

Determine the values of a, b and c for which the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{\sin (a+1)x+\sin x}{x} & \quad ,\;x<0 \\ c & \quad ,\;x=0 \\ \Large\frac{\sqrt{x+bx^2}-\sqrt x}{b\sqrt{x^3}} & \quad ,\;x>0 \end{array} \right. $ may continuous at x = 0

asked Jan 25, 2013 by meena.p

1 answer

Show that the function $ f(x)= \left\{ \begin{array}{1 1} x+\lambda, & \quad x< 1 \\ \lambda x^2+1, & \quad x\geq1 \end{array} \right. $ is continuous function, regardless of the choice of $ \lambda \in R $

asked Jan 25, 2013 by meena.p

1 answer

Show that Sin | x | is continuous.

asked Jan 25, 2013 by meena.p

1 answer

Show that the function : $f(x)= \left\{ \begin{array}{1 1} |x|, & \quad x\leq2 \\ [x], & \quad x>2 \end{array} \right. $ is continuous [0,2].

asked Jan 25, 2013 by meena.p

1 answer

Find a and b if the function :$ f(x)= \left\{ \begin{array}{1 1} [1+| \sin x | ]^{\Large\frac{a}{\sin |x|}}, & \quad \Large\frac{-\pi}{6}< \normalsize x<0 \\ 6 & \quad ,x=0 \\ e^{\Large\frac{\tan 2x}{\tan 3x}}, & \quad 0<x<\Large\frac{\pi}{6} \end{array} \right. $ is continuous on $\bigg(\Large\frac{-\pi}{6},\frac{\pi}{6}\bigg).$

asked Jan 25, 2013 by meena.p

0 answers

Let n be a fixed positive integer.Define a relation R in Z as follows: a,b E\inE Z, aRb if and only if a-b is divisible by n. Show that R is an equivalence relation.

asked Dec 20, 2012 by sreemathi.v

1 answer

Each of the following defines a relation on N : \begin{array}{1 1} (i)\quad x\; is\; greater\; than\; y,x,y\quad N\\(ii)\quad x+y=10,x,y\quad N\\(iii)\quad x\;y\;is\;square\; of\; an\; integer\;x,y\quad N\\(iv)\quad x+4y=10\;x,y\quad N\end{array}Determine which of the above relations are reflexive,symmetric and transitive.

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $A=[-1,1].$ Then,dicuss whether the following functions defined on $A$ are one-one,onto or bijective:$\; f(x)\;=\;\frac{x}{2} $

asked Dec 18, 2012 by sreemathi.v

1 answer

Let A=R-{3},B=R-{1}.Let $f \;:\;A \rightarrow B$ be defined by $f(x)=\Large{\frac{x-2}{x-3}}\normalsize \forall x \in A$.Then show that f is bijective.

asked Dec 18, 2012 by sreemathi.v

1 answer

Given A={2,3,4},B={2,5,6,7}.Construct an example of each of the following:\begin{array}{1 1}(a)\quad an\;injective\;mapping\;from\;A\;to\;B\\(b)\quad a\; mapping\;from\;A\;to\;B\;which\;is\;not\;injective\\(c)\quad a\;mapping\;from\;B\;to\;A \end{array}

asked Dec 18, 2012 by sreemathi.v

1 answer

Let $R$ be relation defined on the set of natural number $N$ as follows:\[R=\{(x,y):x\;\;\;N,y\;\;\;N,2x+y=41\}.\]Find the domain and range of the relation R.Also verify whether R is reflexive,symmetric and transitive.

asked Dec 18, 2012 by sreemathi.v

1 answer

If A={1,2,3,4},define relations on A which have properties of being:\begin{array}{1 1}(a)\quad reflexive,transitive\;but\;not\;symmetric & \;\\(b)\quad symmetric\; but \;neither\;reflexive\;nor\;transitive & \;\\(c)\quad reflexive,symmetric\;and\;transitive\end{array}

asked Dec 18, 2012 by sreemathi.v

1 answer

Let $f\;:\;R\rightarrow R$ be the function defined by $f(x)=\frac{1}{2-\cos x}\forall x\;\in R.$Then,find the range of f.

asked Dec 18, 2012 by sreemathi.v

1 answer

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