Recent questions tagged sec-b

Evaluate : \[ (i) \int \: (x-3) \sqrt {x^2+4x+3} dx \] \[ (ii) \int \: (3x+5) \sqrt {2x^2+3x+7} dx \] \[ (iii) \int \: (x-4) \sqrt {4+x-x^2} dx \] \[ (iv) \int \: (5x-1) \sqrt {6+5x-2x^2} dx \]

asked Jan 2, 2013 by thanvigandhi_1

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Evaluate : $ \int \: \large\frac{1}{\cos(x+a)\cos(x+b)}$$dx $

asked Jan 2, 2013 by thanvigandhi_1

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Evaluate : $ \int \:\large \frac{e^x}{(1+e^x)(2+e^x)}$$dx. $

asked Jan 2, 2013 by thanvigandhi_1

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For any three vectors : $ \overrightarrow a, \overrightarrow b \: and \: \overrightarrow c $ prove that $ \bigg[ \overrightarrow a + \overrightarrow b \: \: \overrightarrow b + \overrightarrow c \: \overrightarrow c + \overrightarrow a \bigg] = 2 \bigg[ \overrightarrow a \: \overrightarrow b \: \overrightarrow c \bigg]. $

asked Jan 2, 2013 by thanvigandhi_1

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Find the vector and cartesian equation of the sphere described on the join of the points (2, -3, 4 ) and (-5, 6, -7 ) as the extremities of a diameter.

asked Jan 2, 2013 by thanvigandhi_1

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If $x=\sin t$ and $y=\sin pt$, prove that $(1-x^2)\large \frac{d^2y}{dx^2}$$-x\large\frac{dy}{dx}+\normalsize p^2y=0$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find the root of the perpendicular drawn from the point P(1, 6, 3) on the line $\large \frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}. $ Also, find its distance from P.

asked Jan 2, 2013 by thanvigandhi_1

0 answers

12 cards, numbered 1 to 12, are placed in a box, mixed up throughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 3, find the probability that it is an even number.

asked Jan 2, 2013 by thanvigandhi_1

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If $x^my^n=(x+y)^{m+n}$,Prove that $(i)\;\large\frac{dy}{dx}=\frac{y}{x}$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find the values of p and q so that $f(x)=\left \{\begin{array}{1 1}x^2+3x+p, & if \;x\leq\;1\\qx+2, & if\;x>\;1\end{array}\right.$is differentiable at $x=1.$

asked Jan 2, 2013 by sreemathi.v

1 answer

Using mean value theorem,prove that there is a point on the curve $y=2x^2-5x+3$ between the points $A(1,0)$ and $B(2,1)$where tangent is parallel to chord $AB$. Also find the point.

asked Jan 2, 2013 by sreemathi.v

1 answer

Find a point on the curve $y=(x-3)^2$,where the tangent is parallel to the chord joining the point (3,0) and (4,1).

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\sqrt {25-x^2}\;in\;[1,5].$

asked Jan 2, 2013 by sreemathi.v

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Verify mean value theorem for each of the function $f(x)=\sin x-\sin 2x\;in\;[0,\pi].$

asked Jan 2, 2013 by sreemathi.v

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Verify mean value theorem for each of the function $f(x)=x^3-2x^2-x+3\;in\;[0,1].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\large\frac{1}{4x-1}$ in $[1,4].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Using Rolle's theorem,find the point on the curve $y=x(x-4),x\in[0,4]$,where the tangent is parallel to $x$-axis.

asked Jan 2, 2013 by sreemathi.v

1 answer

Find the points on the curve $y=(\cos x-1)$ in [0,2$\pi$],where the tangent is parallel to $x$-axis.

asked Jan 2, 2013 by sreemathi.v

1 answer

Discuss the applicability of Rolle's theorem on the function given by $f(x)=\left \{\begin{array}{1 1}x^2+1, & if\;0\leq x\leq1\\3\;x, & if\;1<x<2\end{array}\right.$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=\sqrt {4-x^2}\;in\;[-2,2]$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=x(x+3)e^{\large-x/2}\;in\;[-3,0]$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $log(x^2+2)-log 3\;in\;[-1,1]$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=\sin^4x+\cos^4x\;in\;\begin{bmatrix}0,\large\frac{\pi}{2}\end{bmatrix}$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=x(x-1)^2\;in\;[0,1]$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $y=\tan^{-1}x$, find $\large {\frac{d^2y}{dx^2}}$ in terms of y alone.

asked Jan 2, 2013 by sreemathi.v

1 answer

If $\sqrt {1-x^2}+\sqrt {1-y^2}=a(x-y),$prove that $\large \frac{dy}{dx}=\frac{\sqrt{1-y^2}}{\sqrt{1-x^2}}$.

asked Jan 2, 2013 by sreemathi.v

1 answer

If $x\sin(a+y)+\sin a\cos(a+y)=0,prove\;that\;\large {\frac{dy}{dx}=\frac{\sin^2(a+y)}{\sin a}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $y=(\cos x)^{\Large(\cos x)^{(\Large \cos x)..........\infty.}},$show that $\large {\frac{dy}{dx}=\frac{y^2\tan x}{ylog\cos x-1}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $y^{\large x}=e^{\large y-x},prove\;that\;\large {\frac{dy}{dx}=\frac{(1+logy)^2}{log y}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

(i) Is the binary operation * defined on set N, given a * b = $ \large\frac{a+b}{2} $ for all a, b $ \in$ N, comutative? (ii) Is the above binary operation * associative ?

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Differentiate $ tan^{-1}\bigg (\Large \frac{\sqrt {1+x^2}-1}{x}\bigg)\;\normalsize w.r.t\;\tan^{-1}x\;when\;x\neq 0$

asked Jan 1, 2013 by sreemathi.v

1 answer

Differentiate $\large \frac{x}{\sin x}\;\normalsize w.r.t\;\sin x.$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=3\sin t-\sin 3t,y=3\cos t-\cos 3t,find \;\large \frac{dy}{dx}\;\normalsize at \;t=\large \frac{\pi}{3}$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=a\sin 2t(1+\cos 2t)\;and\;y=b\cos 2t(1-\cos 2t),show\;that\bigg(\large \frac{dy}{dx}\bigg)_{at\;t=\frac{\pi}{4}}=\frac{-b}{a}$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=e^{\large\cos 2t}\; and\;y=e^{\large\sin 2t},prove\;that\;\large \frac{dy}{dx}=\frac{-ylog x}{xlog y}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=\large\frac{1+log t}{t^2},$$y=\large\frac{3+2log t}{t}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $\sin x=\large\frac{2t}{1+t^2},$$\tan y=\large\frac{2t}{1-t^2}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\tan^{-1}\Large {\bigg(\frac{\sqrt {1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\bigg)},\normalsize -1 < x < 1,x\neq 0$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$: $(x+1)^2(x+2)^3(x+3)^4$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\sin^{-1}\bigg|\large\frac{1}{\sqrt {x+1}}\bigg|$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\sin\sqrt x+\cos^2\sqrt x$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $log\begin{bmatrix}log\bigg(log x^5\bigg)\end{bmatrix}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $log\bigg(x+\sqrt{ x^2+a}\bigg)$.

asked Dec 31, 2012 by sreemathi.v

1 answer

A function $f\;:\;R\rightarrow R$ satisfies the equation $f(x+y)=f(x)f(y)$ for all $x,y\in R,f(x)\neq 0.$ Suppose that the function is differentiable at $x=0$ and $f'(0)=2$.Prove that $f'(x)=2f(x).$

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the differentiability of f,where f is defined by $f(x)=\left \{\begin{array}{1 1}1+x, & if\;x\leq 2\\5-x, & if\;x>2\end{array}\right.$at $x=2$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the differentiability of $f$,where $f$ is defined by $f(x)=\left \{\begin{array}{1 1}x^2\sin\large\frac{1}{x}, & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$at $x=0$

asked Dec 31, 2012 by sreemathi.v

1 answer

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

asked Dec 31, 2012 by sreemathi.v

1 answer

Find all points of discontinuity of the function $f(t)=\large\frac{1}{t^2+t-2},$where $\;t=\large\frac{1}{x-1}.$

asked Dec 31, 2012 by sreemathi.v

1 answer

Given the function $ f(x)=\large\frac{1}{x+2}.$Find the points of discontinuity of the composite function $y=f(f(x)).$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find the values of $a$ and $b$ such that the function $f$ defined by $f(x)=\left \{\begin{array}{1 1}\large\frac{x-4}{|x-4|}\normalsize+a, & if\;x<4\\a+b, & if\;x=4\\\large\frac{x-4}{|x-4|}\normalsize +b, & if\;x>4\end{array}\right.$ is a continuous function at $x=4.$

asked Dec 31, 2012 by sreemathi.v

1 answer

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