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Recent questions tagged q2

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x^{3}-12x+1 ,[-3 , 5]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=1-2x-x^{2}, [-4 , 1 ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x^{2}-2x+2 , [0 , 3 ]$

asked May 5, 2013 by poojasapani_1

1 answer

Prove that $\log _e x $ is strictly increasing function on $(0 ,\infty)$.

asked May 4, 2013 by poojasapani_1

1 answer

If $f(1)=10$ and $f '(x)\geq 2 $ for $1\leq x \leq 4 $ how small can $f(4)$ possibly be?

asked May 4, 2013 by poojasapani_1

1 answer

Using Rolle's theorem find the points on the curve $y=x^{2}+1,-2\leq x \leq 2$ where the tangent is parallel to $x$- axis.

asked May 3, 2013 by poojasapani_1

1 answer

Find the point on curve $x^{2}-y^{2}=2$ at which the slope of the tangent is $2$

asked May 1, 2013 by poojasapani_1

1 answer

A particle of unit mass moves so that displacement after $t$ secs is given by $x=3\cos(2t-4).$ Find the acceleration and kinetic energy at the end of $2 \;secs.[ K.E =\large\frac{1}{2}$$mv^{2}\quad m $ is mass]

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the length of the curve $x=a(t-\sin t),y=a(1-\cos t)$ between $t=0$and $\pi$.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the area of the region bounded by the lines $x-2y-12=0 $ and $y$-axis,$y=-1$ and $y=-3$

asked Apr 27, 2013 by poojasapani_1

1 answer

Find the area of the region bounded by the lines $x-2y-12=0 $ and $y$-axis,$y=2$ and $y=5$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate: $\int\limits_{0}^{\large\frac{\pi}{2}}\cos^{9} x dx $

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate: $\int\limits_{0}^{\large\frac{\pi}{2}}\sin^{6}x dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using properties of integration: $\int\limits_{\large\frac{-\pi}{4}}^{\large\frac{\pi}{4}}x^{3}\cos^{3} xdx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\large\frac{\pi}{2}}\cos^{3}x dx$

asked Apr 26, 2013 by poojasapani_1

1 answer

If$\;u=e^{y}\sin y\frac{x}{y}+e^{y}\cos x \frac{y}{x},$ Show that $x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=o$

asked Apr 25, 2013 by poojasapani_1

0 answers

If $u= e^{\large\frac{x}{y}}\sin\frac{x}{y}+e^{\large\frac{y}{x}}\cos\frac{y}{x},$ Show that $ x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=u$

asked Apr 25, 2013 by poojasapani_1

1 answer

If $u=\sqrt{x^{2}+y^{2}},$ Show that $ x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=u$

asked Apr 25, 2013 by poojasapani_1

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$\[\]$y=\cos$$x,x=\large\frac{\pi}{6},$$dx=0.05$

asked Apr 24, 2013 by poojasapani_1

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$\[\]$y=\sqrt{1-x},x=0,dx=0.02$

asked Apr 24, 2013 by poojasapani_1

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$\[\]$y=(x^{2}+5)^{3},x=1,dx=0.1$

asked Apr 24, 2013 by poojasapani_1

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$\[\]$y$=$x^{4}-3x^{2}+x-1,x$$=2,dx$$=0.1$

asked Apr 24, 2013 by poojasapani_1

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$\[\] $y$$=1-x^{2},x$$=5,dx$$=\large\frac{1}{2}$

asked Apr 24, 2013 by poojasapani_1

1 answer

Trace the curve: $y^{2}$$=x^{2}(1-x^{2})$

asked Apr 24, 2013 by poojasapani_1

1 answer

If $Z$ is a standard normal variate. Find the value of $c$ for the following $P(Z > c)=0.85$

asked Apr 22, 2013 by poojasapani_1

1 answer

If $Z$ is a standard normal variate. Find the value of $c$ for the following $P(-c < Z < c)=0.40$

asked Apr 22, 2013 by poojasapani_1

1 answer

If $Z$ is a standard normal variate. Find the value of $c$ for the following $ P(0< Z < c)=0.25$

asked Apr 22, 2013 by poojasapani_1

1 answer

Using binomial expansion,calculate the value of $(98)^{\large\frac{1}{2}}$ correct to three places of decimal.

asked Apr 22, 2013 by sreemathi.v

0 answers

Prove by the method of mathematical induction that $\large\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+....+\frac{1}{(3n+1)(3n+4)}=\frac{n}{4(3n+4)}$,for all $n\in N$.

asked Apr 22, 2013 by sreemathi.v

0 answers

If the probability of a defective fuse from a manufactuning unit is $2\%$ in a box of $200$ fuses find the probability that more than $3$ fuses are defective$ [e^{-4}=0.0183].$

asked Apr 21, 2013 by poojasapani_1

1 answer

If the probability of a defective fuse from a manufactuning unit is $2\%$ in a box of $200$ fuses find the probability that exactly $4$ fuses are defective

asked Apr 21, 2013 by poojasapani_1

1 answer

A die is thrown $120$ times and getting $1$ or $5$ is considered a success.Find the mean and variance of the number of successes.

asked Apr 20, 2013 by poojasapani_1

1 answer

Find the expected value of the number on a die when thrown.

asked Apr 20, 2013 by poojasapani_1

1 answer

If $C_0,C_1,C_2..........C_n$ denote the coefficient of successive terms in the expansion of the binomial $(1+x)^n$ prove that $C_0+C_2+C_4+.........=C_1+C_3+C_5+.....=2^{n-1}$

asked Apr 18, 2013 by sreemathi.v

0 answers

If $x\neq y\neq z$ and $\begin{vmatrix}x& x^2 & 1+x^3\\y & y & 1+y^3\\z & z^2 & 1+z^3\end{vmatrix}=0$.Then show that $xyz=-1$.

asked Apr 18, 2013 by sreemathi.v

0 answers

Given the matrix $A=\begin{vmatrix}1 & 0 & 2\\-2 & 1 & 0\\0 & -1 & 2\end{vmatrix}$,compute $A^{-1}$.

asked Apr 17, 2013 by sreemathi.v

0 answers

Using properties of determinants,show that $\begin{vmatrix}a^2+1 & ab & ac\\ba & b^2+1 & bc\\ca & cb & c^2+1\end{vmatrix}=a^2+b^2+c^2+1$

asked Apr 17, 2013 by sreemathi.v

0 answers

The sum of Rs $1000$ is compounded continuously, the nominal rate of interest being four percent per annum. In how many years will the amount be twice the original principal ? $(\log_{e}$$2=0.6931)$

asked Apr 17, 2013 by poojasapani_1

1 answer

Find the adjoint of the matrix A=$\begin{bmatrix}1 & 0 & -1\\3 & 4 & 5\\0 &-6 &-7\end{bmatrix}$ and hence find the matrix $A^{-1}$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Show that : $\begin{vmatrix}1 & 1 & 1\\{\alpha}^2 &{\beta}^2 &{\gamma}^2\\{\alpha}^3 &{\beta}^3 &{\gamma}^3\end{vmatrix}=(\alpha-\beta)(\beta-\gamma)(\gamma-\alpha)(\alpha\beta+\beta\gamma+\alpha\gamma)$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Solve the following differential equation;$(D^{2}-4D+13)$y$=e^{-3x}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $\large\frac{dy}{dx}+\frac{4x}{x^{2}+1}$$y=\large \frac{1}{(x^{2}+1)^{2}}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following system of equations using matrices : $x+y+z=6,x-y+z=2,2x+y-z=1$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Using the properties of determinants ,show that $\begin{vmatrix}x-y-z & 2x & 2x\\2y & y-z-x & 2y\\2z & 2z & z-x-y\end{vmatrix}=(x+y+z)^3$

asked Apr 16, 2013 by sreemathi.v

0 answers

Solve the following $\large\frac{dy}{dx}$=$\large\frac {y(x-2y)}{x(x-3y)}$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\cos^{2}xdy +ye^{\tan x }dx=0 $

asked Apr 15, 2013 by poojasapani_1

1 answer

Form the differential equuations by eliminating arbitary constants given in brackets against each. $y=Ae^{2x} \cos (3x , +B ) [A , B ]$

asked Apr 15, 2013 by poojasapani_1

1 answer

If $A=\begin{vmatrix}1 & -2 & -3\\2 & 3 & 2\\3 &-3 & -4\end{vmatrix},$find $A^{-1}$ and hence solve the following system of linear equations : $x+2-3z=-4,2x+3y+2z=2,3x-3y-4z=11.$

asked Apr 15, 2013 by sreemathi.v

0 answers

Form the differential equuations by eliminating arbitary constants given in brackets against each $y=e^{mx} [m] $

asked Apr 15, 2013 by poojasapani_1

1 answer

Form the differential equuations by eliminating arbitary constants given in brackets against each. $y= e^{3x}(C \cos 2x +D \sin 2x ) [C , D ]$

asked Apr 15, 2013 by poojasapani_1

1 answer

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