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Recent questions tagged p13

Solve by matrix inversion method following system of linear equation$\;x-3y-8z+10=0\;,3x+y=4\;,2x+5y+6z=13$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation $2x-y+z=7\;,3x+y-5z=13\;,x+y+z=5$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation $\;x+y+z=9\;,\;2x+5y+7z=52\;,2x+y-z=0$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation $\;7x\;+\;3y\;=\;-1\;,\;2x\;+\;y\;=\;0$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation:$\;2x\;-\;y\;=7\;,\;3x\;-2y\;=11$

asked Mar 29, 2013 by poojasapani_1

1 answer

Prove that $ \Large\frac{d}{dx}\bigg[\Large\frac{1}{4 \sqrt 2} \normalsize log\bigg|\Large\frac{x^2+\sqrt 2 x+1}{x^2- \sqrt 2 x+1} \bigg|+\Large\frac {1}{2 \sqrt 2} \normalsize \tan^{-1} \Large\frac{\sqrt 2 x}{1-x^2}\bigg]=\Large\frac{1}{1+x^4}$

asked Jan 25, 2013 by meena.p

1 answer

Let $y= \tan^{-1}\bigg[\Large\frac{4x}{1+5x^2}\bigg] \normalsize +\tan^{-1}\bigg[\Large\frac{2+3x}{3-2x}\bigg],$ show that $ \Large\frac{dy}{dy}=\frac{5}{1+25x^2}$

asked Jan 25, 2013 by meena.p

1 answer

Given that $ \cos \frac{x}{2}.\cos \frac{x}{4}.\cos \frac{x}{8}.......=\Large\frac {\sin x}{x},$ \[Prove\;that\;\frac{1}{2^2}\sec^2\frac{x}{2}+\frac{1}{2^4}\sec^2\frac{x}{4}+.......=cosec^2x-\frac{1}{x^2}\]

asked Jan 25, 2013 by meena.p

1 answer

Find $\Large\frac{dy}{dx},$ when $y=\sin^{-1}\bigg[x\sqrt{1-x}-\sqrt x \sqrt{1-x^2}\bigg]$

asked Jan 25, 2013 by meena.p

1 answer

Differentiate w.r.t. x, $ y=\tan^{-1}\bigg[\Large\frac{a\cos x-b\sin x}{b\cos x+a \sin x}\bigg]$

asked Jan 25, 2013 by meena.p

1 answer

If $ y=\frac{2}{\Large\sqrt {a^2-b^2}}\tan^{-1}\bigg[\sqrt{\frac{a-b}{a+b}}\tan \frac{x}{2} \bigg],$ prove that $ \Large\frac{dy}{dx}=\frac{1}{a+b \cos x}, \normalsize a>b>0 $

asked Jan 25, 2013 by meena.p

1 answer

If $y=\sin ^{-1}\big [x^2\sqrt{1-x^2}+x\sqrt {1-x^4}\big],$ prove that $ \Large\frac{dy}{dx}=\frac{2x}{\sqrt{1-x^4}}+\frac{1}{\sqrt{1-x^2}}$

asked Jan 25, 2013 by meena.p

1 answer

Find$ \Large\frac{dy}{dx}\;\normalsize when\;y=\sin ^{-1} \bigg[\Large\frac{5x+12 \sqrt{1-x^2}}{13}\bigg]$

asked Jan 25, 2013 by meena.p

1 answer

Let $\phi(x)\;andh(x)$ be derivable at x = c. Show that necessary and sufficient condition for the function defined as :\[f(x)= \left\{ \begin{array}{1 1} \phi(x), & \quad x \leq c \\ h(x), & \quad x>c \end{array} \right. \]to be derivable at x= c are $(i)\phi(c)=h(c)\quad(ii)\phi'(c)=h'(c)$

asked Jan 25, 2013 by meena.p

1 answer

Let $f(x) = \left\{ \begin{array}{l l} \Large\frac{1-sin^3x}{3cos^2x}, & \quad if\; { x < \Large\frac{\pi}{2}}\\ a, & \quad if\; { x = \Large\frac{\pi}{2}} \\ \Large\frac{b(1-sin x)}{(\pi - 2x)^2}, & \quad if \;{ x > \Large\frac{\pi}{2}} \end{array}. \right.$ If f(x) is continuous function at x \( x = \Large\frac{\pi}{2} \), find a and b.

asked Jan 25, 2013 by meena.p

1 answer

Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b.Then R is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $aRb$. If a is congruent to b where $a,b\in T$, then $R$ is:

asked Dec 19, 2012 by sreemathi.v

1 answer

Let * be binary operation defined on R by $ ab=1+ab, a,b \in R.$ Then the operation is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $\ast $ be the binary operation defined on Q.Find which of the following binary operations are commutative\begin{array}{1 1}(i)\;a \ast b=a-b\quad a,b\in Q & (ii)\;a \ast b=a^2+b^2\quad a,b\in Q\\(iii)\;a \ast b=a+ab\quad a,b\in Q & (iv)\;a \ast b=(a-b)^2\quad a,b\in Q\end{array}

asked Dec 19, 2012 by sreemathi.v

1 answer

Functions $ f,g:R \rightarrow R $ are defined,respectively,by $f(x)=x^2+3x+1,g(x)=2x-3,$ find\[(i)\quad f\; o\; g\qquad(ii)\quad g\;o\;f\qquad(iii)\quad f\;o\;f\qquad(iv)\quad g\;o\;g\]

asked Dec 19, 2012 by sreemathi.v

1 answer

Using the definition,prove that the function $f:\;A\rightarrow B$ is invertible if and only if f is both one-one and onto.

asked Dec 19, 2012 by sreemathi.v

1 answer

Let A={1,2,3....9} and R be the relation in AxA defined by (a,b)R(c,d) if a+d=b+c for (a,b),(c,d) in AxA.Prove that R is an equivalence relation and also obtain the equivalent class[(2,5)].

asked Dec 19, 2012 by sreemathi.v

1 answer

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