Recent questions tagged p166

Find all the values of $\bigg(\large\frac{1}{2}$$-i\large\frac{\sqrt 3}{2}\bigg)^{\Large\frac{3}{4}}$ and hence prove that the product of the values is 1.

asked Jun 13, 2013 by sreemathi.v

1 answer

Solve : $x^4-x^3+x^2-x+1=0$

asked Jun 13, 2013 by sreemathi.v

1 answer

Solve : $x^4+4=0$

asked Jun 12, 2013 by sreemathi.v

1 answer

Prove that if $\omega^3=1$,then (iii) $\large\frac{1}{1+2\omega}-\frac{1}{1+\omega}+\frac{1}{2+\omega}$$=0$

asked Jun 12, 2013 by sreemathi.v

1 answer

Prove that if $\omega^3=1$,then (ii) $\bigg(\large\frac{-1+i\sqrt 3}{2}\bigg)^5+\bigg(\large\frac{-1-i\sqrt 3}{2}\bigg)^5$$=-1$

asked Jun 12, 2013 by sreemathi.v

1 answer

Prove that if $\omega^3=1$,then (i) $(a+b+c)(a+b\omega+c\omega^2)(a+b\omega^2+c\omega)=a^3+b^3+c^3-3abc$

asked Jun 12, 2013 by sreemathi.v

1 answer

If $x=a+b$,$y=a\omega+b\omega^2,z=a\omega^2+b\omega$ show that (ii) $x^3+y^3+z^3=3(a^3+b^3)$ where $\omega$ is the complex cube root of unity.

asked Jun 12, 2013 by sreemathi.v

1 answer

If $x=a+b$,$y=a\omega+b\omega^2,z=a\omega^2+b\omega$ show that (i) $xyz=a^3+b^3$ where $\omega$ is the complex cube root of unity.

asked Jun 12, 2013 by sreemathi.v

1 answer

Find all the value of the following : $(-\sqrt 3-i)^{\large\frac{2}{3}}$

asked Jun 12, 2013 by sreemathi.v

1 answer

Find all the value of the following : $(8i)^{\large\frac{1}{3}}$

asked Jun 12, 2013 by sreemathi.v

1 answer

Find all the value of the following : $(i)^{\large\frac{1}{3}}$

asked Jun 12, 2013 by sreemathi.v

1 answer

Differentiate the following functions with respect to $x:\; sinx(ax+b)$

asked Apr 4, 2013 by balaji.thirumalai

1 answer

$ \int\tan^{-1}\sqrt x$ is equal to which of the following options:

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{\cos 2x-\cos 2\theta}{\cos x-\cos\theta}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;2(\sin x+x\cos\theta)+C & (B)\;2(\sin x-x\cos\theta)+C\\(C)\;2(\sin x+2x\cos\theta)+C & (D)\;2(\sin x-2x\cos\theta)+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_ {\Large\frac{-\pi}{4}}^{\Large\frac{\pi}{4}} \log(\sin x+\cos x)dx$

asked Jan 15, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_0^{\Large \pi} x \log \sin xdx$

asked Jan 15, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^1 x\;log(1+2x)dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_0^{\Large\frac{\pi}{2}}\large\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^2}\quad\normalsize \text{(Hint:Divide Numerator and Denominator by $\cos^4x)$}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate :$\int \sqrt \tan x \;dx\;$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int e^{-3x}\cos^3xdx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_{\Large \frac{\pi}{3}}^{\Large \frac{\pi}{2}}\large\frac{\sqrt{1+\cos x}}{(1-\cos x)^{\large\frac{5}{2}}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\sin^{-1}\sqrt{\large\frac{x}{a+x}}dx\quad(Hint:Put\;x=a\tan^2\theta)$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int e^{\tan^{-1}x}\bigg(\frac{1+x+x^2}{1+x^2}\bigg)dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Prove that the greatest integer function defined by $ f(x) = [x], 0<x<3$ is not differentiable at $x = 1 $ and $ x = 2 $

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Prove that the function $ f $ given by $f(x) = | x - 1 |, x \in R\;$ is not differentiable at $\; x = 1$.

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Differentiate the functions with respect to x in $\;\cos(\sqrt {x} \;) $

asked Nov 8, 2012 by thanvigandhi_1

1 answer

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

asked Nov 8, 2012 by thanvigandhi_1

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

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

Ask Questions, Get Answers

Find all the values of $\bigg(\large\frac{1}{2}$$-i\large\frac{\sqrt 3}{2}\bigg)^{\Large\frac{3}{4}}$ and hence prove that the product of the values is 1.

Solve : $x^4-x^3+x^2-x+1=0$

Solve : $x^4+4=0$

Prove that if $\omega^3=1$,then (iii) $\large\frac{1}{1+2\omega}-\frac{1}{1+\omega}+\frac{1}{2+\omega}$$=0$

Prove that if $\omega^3=1$,then (ii) $\bigg(\large\frac{-1+i\sqrt 3}{2}\bigg)^5+\bigg(\large\frac{-1-i\sqrt 3}{2}\bigg)^5$$=-1$

Prove that if $\omega^3=1$,then (i) $(a+b+c)(a+b\omega+c\omega^2)(a+b\omega^2+c\omega)=a^3+b^3+c^3-3abc$

If $x=a+b$,$y=a\omega+b\omega^2,z=a\omega^2+b\omega$ show that (ii) $x^3+y^3+z^3=3(a^3+b^3)$ where $\omega$ is the complex cube root of unity.

If $x=a+b$,$y=a\omega+b\omega^2,z=a\omega^2+b\omega$ show that (i) $xyz=a^3+b^3$ where $\omega$ is the complex cube root of unity.

Find all the value of the following : $(-\sqrt 3-i)^{\large\frac{2}{3}}$

Find all the value of the following : $(8i)^{\large\frac{1}{3}}$

Find all the value of the following : $(i)^{\large\frac{1}{3}}$

Differentiate the following functions with respect to $x:\; sinx(ax+b)$

$ \int\tan^{-1}\sqrt x$ is equal to which of the following options:

$\Large \int\frac{\cos 2x-\cos 2\theta}{\cos x-\cos\theta}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;2(\sin x+x\cos\theta)+C & (B)\;2(\sin x-x\cos\theta)+C\\(C)\;2(\sin x+2x\cos\theta)+C & (D)\;2(\sin x-2x\cos\theta)+C\end{array}

Evaluate the following:$\int\limits_ {\Large\frac{-\pi}{4}}^{\Large\frac{\pi}{4}} \log(\sin x+\cos x)dx$

Evaluate the following:$\int\limits_0^{\Large \pi} x \log \sin xdx$

Evaluate the following: $\int\limits_0^1 x\;log(1+2x)dx$

Evaluate the following:$\int\limits_0^{\Large\frac{\pi}{2}}\large\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^2}\quad\normalsize \text{(Hint:Divide Numerator and Denominator by $\cos^4x)$}$

Evaluate :$\int \sqrt \tan x \;dx\;$

Evaluate the following:$\int e^{-3x}\cos^3xdx$

Evaluate the following:$\int\limits_{\Large \frac{\pi}{3}}^{\Large \frac{\pi}{2}}\large\frac{\sqrt{1+\cos x}}{(1-\cos x)^{\large\frac{5}{2}}}$

Evaluate the following:$\int\sin^{-1}\sqrt{\large\frac{x}{a+x}}dx\quad(Hint:Put\;x=a\tan^2\theta)$

Evaluate the following: $\int e^{\tan^{-1}x}\bigg(\frac{1+x+x^2}{1+x^2}\bigg)dx$

Prove that the greatest integer function defined by $ f(x) = [x], 0<x<3$ is not differentiable at $x = 1 $ and $ x = 2 $

Prove that the function \( f \) given by $f(x) = | x - 1 |, x \in R\;$ is not differentiable at $\; x = 1$.

Differentiate the functions with respect to x in $\;\cos(\sqrt {x} \;) $

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

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

Differentiate the functions with respect to $x: \large \frac{ sin\; (ax + b) } { cos \;( cx + d)} $

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

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

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