Recent questions tagged exemplar

Differentiate the following w.r.t $x$ : $\sin (x^2)+\sin^2x+\sin^2(x^2)$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\cos\bigg(\tan\sqrt {x+1}\bigg)$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\sin^n(ax^2+bx+c)$.

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

Differentiate the following w.r.t $x$ :$\large \frac{8^x}{x^8}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$: $2^{\large \cos^2x}$

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

Show that $f(x)=|x-5|$ is continuous but not differentiable at $x=5$

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

Examine the differentiability of f,where f is defined by $f(x)=\left \{\begin{array}{1 1}x[x], & if\;0\leq x<2\\(x-1)x, & if\;2\leq x<3\end{array}\right.$at $x=2$

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

Prove that the function f defined by $ f(x)=\left \{\begin{array}{1 1}\large\frac{x}{\mid x\mid+2x^2}, & x\neq 0\\k, &x=0\end{array}\right.$remains discontinuous at x=0,regardless the choice of k.

asked Dec 31, 2012 by sreemathi.v

1 answer

Find the value of $k$ in the following so that the function $f$ is continuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{1-\cos kx}{x\sin x}, & if\;x\neq 0\\\large\frac{1}{2}, & if\;x=0\end{array}\right.\;at\;x=0$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find the value of $k$ in the following so that the function $f$ is continuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{\sqrt {1+kx}-\sqrt{1-kx}}{x}, & if\;-1\leq x< 0\\\large\frac{2x+1}{x-2}, & if\;0\leq x\leq 1\end{array}\right.\; at\; x=0$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find the value of k in the following so that the function $f$ is continuous at the indicated point: $f(x)=\left \{\begin{array}{1 1}\frac{\large 2^{x+2}-16}{4^{\large x}-16}, & if\;x\neq 2\\k, & if\;x=2\end{array}\right.$ at $x=2$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find the value of k in the following so that the function f is continuous at the indicated point $f(x)=\left \{\begin{array}{1 1}3x-8, & if\;x\neq 5\\2k, & if\;x=5\end{array}\right.\;at\;x=5$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find whether f(x) is continuous or discontinuous at the indicated point $f(x)= x ^2+x-1\;at\;x=1.$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find whether $f(x)$ is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{x^2}{2}, & if\;0\leq x\leq 1\\2x^2-3x+\large\frac{3}{2}\normalsize,& if\;0< x\leq 2\end{array}\right.$ at $x=1$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Find whether f(x) is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{e^ {\Large\frac{1}{x}}}{1+e^ {\Large\frac{1}{x}}},\normalsize & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$ at $x=0$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Find whether $f(x)$ is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}( x-a)\sin\large\frac{1}{x-a},\normalsize & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$ at $x=a$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Find whether f(x) is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\mid x\mid\cos\large\frac{1}{x}, \normalsize& if\;x\neq 0\\0, & if\;x=0\end{array}\right.$at x=0.

asked Dec 31, 2012 by sreemathi.v

1 answer

Find whether f(x) is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}x-4, & if\;x\neq 4\\2(x-4)\\0, & if\;x=4\end{array}\right.$at x=4.

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the continuity of f(x) at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{2x^2-3x-2}{x-2} &\normalsize if\;x\neq 2\\5 & if\;x=2\end{array}\right.$ at x=2.

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the continuity of f(x) at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{1-\cos 2x}{x^2} & \normalsize if\;x\neq 0\\5 & if\;x=0\end{array}\right.$at x=0.

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the continuity of f(x) at the indicated point $f(x)=\left \{\begin{array}{1 1}3x+5 & if\;x\geq 2\\x^2 & if\;x<2\end{array}\right.$ at $x=2.$

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the continuity of the function $f(x)=x^3+2x^2-1$ at $x=1$

asked Dec 31, 2012 by sreemathi.v

1 answer

True or False: The maximum value of $\begin{vmatrix}1 & 1 & 1\\1 &(1-\sin x) & 1\\1 & 1 & 1-cos x\end{vmatrix}\;is\;\Large \frac{1}{2}$.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: Let $\begin{vmatrix}a & p & x\\b & q & y\\c & r & z\end{vmatrix}$ = 16, then $\Delta_1=\begin{vmatrix}p+x & a+x & a+p\\q+y & b+y & b+q\\r+z & c+z & c+r\end{vmatrix}$ = 32

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: If the determinant $\small\begin{vmatrix}x+a & p+u & l+ f\\y+b & q+v & m +g\\z+c & r+w & n + h\end{vmatrix}$ splits into exactly $k$ determinants of order $3$, each element of which contains online term,then the value of $k$ is $8$.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: The determinant $ \begin{vmatrix}\sin A & \cos A & \sin A+\cos B\\\sin B & \cos A & \sin B+\cos B\\\sin C & \cos A & \sin C+\cos B\end{vmatrix}$ is equal to zero

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $\mid adj A\mid={\mid A\mid}^2$,where A is a square matrix of order two.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $\begin{vmatrix}x+1 & x+2 & x+a\\x+2 & x+3 & x+b\\x+3 & x+4 & x+c\end{vmatrix}=0,$where a,b,c are in A.P.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: If the value of a third order determinant is 12,then the value of the determinant formed by replacing each element by its co-factor will be 144.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: If A and B are matrices of order 3 and $\mid A\mid=5,\mid B \mid=3,then\mid 3AB\mid=27\times 5\times 3=405$

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $|\;A^{-1}\;|\neq |\;A\;|^{-1}$,where A is non-singular matrix.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $(aA)^{-1}= \Large{ \frac{1}{a}}\normalsize A^{-1}$, where $a$ is a any real number and $A$ is a square matrix.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $(A^3)^{-1}=(A^{-1})^3$,where A is a square matrix and $|\;A\;|\neq 0$

asked Dec 28, 2012 by sreemathi.v

1 answer

If $f(x)$ = $\small\begin{vmatrix}(1+x)^{17} & (1+x)^{19} & (1+x)^{23}\\(1+x)^{23} & (1+x)^{29} & (1+x)^{34}\\(1+x)^{41} & (1+x)^{43} & (1+x)^{47}\end{vmatrix}$ = $A+Bx+Cx^2+.....$, then $A$ =

asked Dec 28, 2012 by sreemathi.v

1 answer

$\begin{vmatrix}0 & xyz & x-z\\y-x & 0 & y-z\\z-x & z-y & 0\end{vmatrix}$ =

asked Dec 28, 2012 by sreemathi.v

1 answer

if $x=-9$ is a root of $\begin{vmatrix}x & 3 & 7\\2 & x & 2\\7 & 6 & x\end{vmatrix}=0$, then other roots are

asked Dec 28, 2012 by sreemathi.v

1 answer

The sum of the products of elements of any row with the co-factors of corresponding elements is equal to ________________.

asked Dec 28, 2012 by sreemathi.v

1 answer

If A is a matrix of order $3\times 3$,then number of minors in determinant of A are____________.

asked Dec 28, 2012 by sreemathi.v

1 answer

If A is a matrix of order $3\times 3$,then $(A^2)^{-1}$=_____________.

asked Dec 28, 2012 by sreemathi.v

1 answer

If $\cos 2\theta=0$, then ${\begin{vmatrix}0 & \cos\theta & \sin\theta\\\cos\theta & \sin\theta & 0\\\sin\theta & 0 & \cos\theta\end{vmatrix}}^2$ =

asked Dec 28, 2012 by sreemathi.v

1 answer

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