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Recent questions tagged p108

Evaluate the determinants: $ \begin{vmatrix} 2&-1&2 \\ 0&2&-1 \\3&-5&0 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Evaluate the determinants: $ \begin{vmatrix} 0&1&2 \\ -1&0&3 \\-2&3&0 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Evaluate the determinants: $ \begin{vmatrix} 3&-4&5 \\ 1&1&-2 \\2&3&1 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

$ \text{Evaluate the determinants: } \text{(ii): } \begin{vmatrix} x^2-x+1&x-1\\x+1&x+1 \end{vmatrix}$

asked Mar 6, 2013 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

Evaluate the determinant: $\begin{vmatrix} 3&-1&-2 \\ 0&0&-1 \\3&-5&0 \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

\[ \text{If A = } \begin{bmatrix} 1&0&1 \\ 0&1&2 \\ 0&0&4 \end{bmatrix}, \text{then show that } |\;3A\;| = 27|\;A\;|\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

\[ \text{If A = } \begin{bmatrix} 1&2 \\ 4&2 \end{bmatrix}, \text{then show that } |\;2A\;| = 4|\;A;|\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Evaluate the determinant: $\begin{vmatrix} cos\theta &-sin\theta \\ sin\theta & cos\theta \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Evaluate the determinant:$ \begin{vmatrix} 2&4 \\ -5&-1 \end{vmatrix} $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

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