Recent questions tagged q15

Differentiate $ \tan^{-1} \{ \large\frac{\sqrt{1+x^2}-1}{x} \}$ w.r.t. $ x$.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If $ y=(\log\: x)^x+(x)^{\large \cos\:x},\: find\: \large\frac{dy}{dx} $.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If $ x=a \bigg( \cos\: \theta +\log \tan\large \frac{\theta}{2} \bigg) $ and $ y = a\sin\: \theta,$ find the value of $ \large\frac{d^2y}{dx^2}$$\: at \: \theta = \large\frac{\pi}{4}.$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Differentiate the following function w.r.t. $ x.$ $ (sin\: x)^{\large cos^{-1}x} $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If $ y=tan^{-1}\left \{\large\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right \} $,find $\large\frac{dy}{dx}.$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Using properties of determinants prove that \[ \begin{vmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{vmatrix}= (ab+bc+ca)^3 \]

asked Feb 7, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} $ find $ A^{-1}$. Using $ A^{-1}$ solve the system of equations:$ 2x-3y+5z=11; 3x+2y-4z=-5; x+y-2z = -3$

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Show that the function $ f(x) = |x+2 | $ is continuous at every $ x \in R$ but fails to be differentiable at x = -2.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Find the points on the curve $ y=x^3$ at which the slope of the tangent is equal to the y - coordinate of the point.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Find the probability that sum of the numbers showing on the two dice is 8, given that atleast one dice doesnt show five.

asked Feb 5, 2013 by meena.p

0 answers

The foot of the perpendicular drawn from the origin to the plane is (2,5,7). FInd the equation of the plane.

asked Feb 5, 2013 by meena.p

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If $\Large\frac{1}{a},\frac{1}{b},\frac{1}{c}$are the $\large p^{th},q^{th}and\;r^{th}\;$ terms of an AP and $ \bar{u}=(q-r)\bar{i}+(r-p)\bar{j}+(p-q)\bar{k}\;and\;\bar{v}=\large\frac{1}{a}\bar{i}+\frac{1}{b}\bar{j}+\frac{1}{c}\bar{k}$ then prove that $\bar{u}\; and\;\bar{v}$ are orthogonal vectors.

asked Feb 4, 2013 by meena.p

1 answer

Solve the differential equation :\[(x^2y+y^2x)dy=(x^3+y^3)dx\]

asked Feb 4, 2013 by meena.p

0 answers

Form the differential equation of the family of parabolas having vertex at the origin and axis along positive y - axis.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find the area of the circle $ x^2+y^2=a^2$

asked Feb 4, 2013 by meena.p

0 answers

Differentiate $ x^{\large xcos\: x}+\large\frac{x^2+1}{x^2-1} $ w.r.t. $ x $.

asked Feb 4, 2013 by thanvigandhi_1

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If $ x=a(\theta-\sin\theta),y=a(1+\cos\theta), $ find $ \large\frac{d^2y}{dx^2} $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If $ y=\sqrt{x^2-1}-\log \bigg( \large\frac{1}{x}+\sqrt{1+\frac{1}{x^2}} \bigg) $ find $\large\frac{dy}{dx} $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If $ y= \bigg( x+\sqrt{x^2-1} \bigg)^m,$ then show that $(x^2+1)\large\frac{d^2y}{dx^2}$$+x\large\frac{dy}{dx}$$-m^2y=0 $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

If $x= \bigg( \cos\theta + \log \tan\large\frac{\theta}{2} \bigg), $$y=\sin\: \theta, \large\frac{d^2y}{dx^2}$$\: at \: \theta=\large\frac{\pi}{4} $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Show that the function $ f(x) = \left\{ \begin{array}{l l}-x^2, & \quad { x \leq 0} \\ x^2, & \quad { x \geq 0} \end{array} \right. $ is continuous at x = 0, also show that f is differentiable at x = 0.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

$\int \sqrt {1+x^2} d(x^2)=$\[(a)\;\frac{2}{3x}(1+x^2)^{3/2}\qquad (b)\;\frac{2}{3}(1+x^2)^{3/2}\qquad(c)\;\frac{2x}{3}(1+x^2)^{3/2}\qquad(d)\;\frac{2x}{3}(1+x^2)\]

asked Jan 31, 2013 by meena.p

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Find $ \large\frac{dy}{dx}, \: if \: x^y+y^x=a^b.$

asked Jan 31, 2013 by thanvigandhi_1

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

asked Jan 30, 2013 by thanvigandhi_1

0 answers

If $ x^py^q=(x+y)^{p+q}$, prove that $ \large\frac{dy}{dx}=\frac{y}{x} $.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate: $\int\limits_0^{\large \pi}\large\frac{dx}{5 + 4\cos x}$

asked Jan 29, 2013 by fingeazy

0 answers

If $ y=x\log \bigg( \large\frac{x}{a+bx} \bigg)$, find $\large\frac{d^2y}{dx^2} $.

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If $ y = e^{\Large m\tan^{-1}x}$, prove that $ (1+x^2)\large\frac{d^2y}{dx^2}$$+(2x-m)\large\frac{dy}{dx}=0.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

The minimum value of f(x) = |3-x| + |2+x| + |5-x| is \[(a)\;0\qquad(b)\;7\qquad(c)\;8\qquad(d)\;10\]

asked Jan 28, 2013 by meena.p

0 answers

Differentiate $ \sin(x^x)+(\sin x)^x,$ with respect to x.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

For the matrix $ A= \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix} $, show that $ A^3-6A^2+5A+11I=0.$ Hence, find $A^{-1}.$

asked Jan 27, 2013 by thanvigandhi_1

0 answers

If $ x\sqrt{1+y} +y\sqrt{1+x}=0, \: find \:\large \frac{dy}{dx} $

asked Jan 27, 2013 by thanvigandhi_1

0 answers

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

asked Jan 27, 2013 by thanvigandhi_1

0 answers

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

Verify Rolle's theorem for the function $ f(x) = e^x\cos \: x\: on \: \bigg[ -\large\frac{\pi}{2}, \frac{\pi}{2} \bigg] $.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

If $ y = [ \log (x+\sqrt{1+x^2} ]^2$, show that $ (1+x^2)\large\frac{d^2y}{dx^2}$$+x\large\frac{dy}{dx}$$-2=0 $

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Check whether the function f (x) =$ x^{100}$ + sin x-1 is strictly increasing or strictly decreasing or none of both on $(-1,1)$ . Should the nature of a man be like this function? Justify your answers

asked Jan 24, 2013 by shanthinig

0 answers

If $ y=x^x+(sin\: x)^x, \: find \: \frac{dy}{dx} $

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Give that x = -9 is a root of $ \begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{vmatrix}=0$ find the other roots. Hint: Evaluate, find other roots.

asked Jan 24, 2013 by meena.p

0 answers

Two cards are drawn one by one without replacement from well shuffled pack of 52 cards. Find the probability distribution of the number of aces.

asked Jan 24, 2013 by thanvigandhi_1

2 answers

Find the probability of number of doublets in three throws of a pair of dice.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Prove that $\sin2[\cot^{-1}\{\cos(\tan^{-1}x)\}]=2\frac{\sqrt{x^2+1}}{x^2+2}$

asked Jan 24, 2013 by meena.p

1 answer

Show that the relation R on N x N defined by $(a,b)R(c,d)\;\Leftrightarrow \; a+d = b+c $is an equivalence relation.

asked Jan 23, 2013 by meena.p

0 answers

If $ y = e^{a\: cos^{-1}x}, -1 \leq x \leq 1, $ show that : $ (1-x^2)\large\frac{d^2y}{dx^2}$$-x\large \frac{dy}{dx}$$-a^2y=0$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

show that the function $ f(x) = \left\{ \begin{array}{l l} \large \frac{3}{2}-x, & \quad {\large\frac{1}{2}< x < 1}\\ \frac{3}{2}, & \quad { x = 1} \\ \large\frac{3}{2}+x, & \quad {1 \leq x < 2} \end{array} \right. $ is continuous at x = 1.

asked Jan 21, 2013 by thanvigandhi_1

0 answers

Find the equation of a curve passing through origin and satisfying the differential equation $(1-x^2)\Large \frac{dy}{dx}\normalsize-2xy=4x^2$

asked Jan 18, 2013 by sreemathi.v

1 answer

Prove that in any triangle ABC,$ cos A=\large \frac{b^2+c^2-a^2}{2bc}$,$where \overrightarrow{a},\overrightarrow{b} and \overrightarrow{c}$ are the vectors of sides BC, CA and AB respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

Differentiate : $\large \frac{x}{a} $$\sqrt {x^2-a^2}+\large\frac{a^2}{2}$$\sin^{-1}\large\frac{x}{a}$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

If $ y=x^{x^{x....^{\infty}}} $, then prove that $ \large\frac{dy}{dx}=\frac{y^2}{x(1-ylog\: x )}$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Examine for continuity the function f' defined by $ f(x) = \left\{ \begin{array}{l l} \large\frac{e^{\large \frac{1}{x}} - 1}{e^{\large\frac{1}{x}} + 1}, & \quad { x \neq 0}\\ 0, & \quad \text{ $x$ = 0} \end{array}. \right. \: at\: x = 0.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

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