Exercise 9B

### Show that sec is a continuous function.

Solution: Assume $f(x)=\sec x$ So, $f(x)=\frac{1}{\cos x}$ $f(x)$ is not defined when $\cos x=0$ And $\cos x=0$ when, $x=\frac{\pi}{2}$ and odd multiples of $\frac{\pi}{2}$ like $-\frac{\pi}{2}$...

### Show that function

Solution: It is given that: $f(x)=\left\{\begin{array}{c} \frac{x^{n}-1}{x-1}, \text { when } x \neq 1 \\ n, \text { when } x=1 \end{array}\right.$ L.H.L. and $\mathrm{x}=1$ \$\begin{array}{l} \lim...

### (i) find the matrix 2A + B. (ii) find a matrix C such that:

(ii) Solution: (i) $2A\text{ }+\text{ }B$ (ii)

### Solve:

Solution: According to the given question, the matrix is

### From given data below find (i) 2A – 3B + C (ii) A + 2C – B

Solution: $\left( i \right)\text{ }2A\text{ }-\text{ }3B\text{ }+\text{ }C$ $\left( ii \right)\text{ }A\text{ }+\text{ }2C\text{ }-\text{ }B$

### Find x and y if: (i) 3[4 x] + 2[y -3] = [10 0]

(ii) Solution: From L.H.S, we have $3\left[ 4\text{ }x \right]\text{ }+\text{ }2\left[ y\text{ }-3 \right]$ $=\text{ }\left[ 12\text{ }3x \right]\text{ }+\text{ }\left[ 2y\text{ }-6 \right]~$...

(ii)   Solution: (i) $3\left[ 5\text{ }-2 \right]\text{ }=\text{ }\left[ 3\times 5\text{ }3x-2 \right]\text{ }=\text{ }\left[ 15\text{ }-6 \right]$ (ii)