If 1&0&0 0&1&0 0&0&1 x = 1 -1 0 , find x, y and z.

Examine the following functions for continuity.
$f(x) = \frac{1}{\text{x}-5}$

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Evaluate the following integrals:
$\int\limits^1_0\frac{2\text{x}}{1+\text{x}^2}\text{ dx}$

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If $2\begin{bmatrix}3&4\\5&\text{x} \end{bmatrix}+\begin{bmatrix}1&\text{y}\\0&1 \end{bmatrix}=\begin{bmatrix}7&0\\10&5 \end{bmatrix},$ find x - y.

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Find the value of x for which $\text{x}\Big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\Big)$ is a unit vector.

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Represent the following graphically:

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Let $f : R \rightarrow R, g : R \rightarrow R$ be two functions defined by $f(x) = x^2 + x + 1$ and $g(x) = 1 - x^2.$ Write fog $(-2).$

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Find the mean of the following probability distribution:

$\text{X}=\text{x}_\text{i}:$	$1$	$2$	$3$
$\text{P}(\text{X}=\text{x}_\text{i}):$	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{5}{8}$

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If $f : R \rightarrow R$ is defined by $f(x) = x^2,$ find $f^{-1}(-25).$

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Write the cartesian and vector equations of x-axis.

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Find the principal values:
$\text{cosec}^{-1}(2)$

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Answer