List of practice Questions

Find all points of discontinuity of f, where f is defined by 

\[f(x) =   \begin{cases}    x^{10}-1,     & \quad \text{if } x{\leq 1}\\     x^2,  & \quad \text{if } x \text{>1}   \end{cases}\]

Find all points of discontinuity of f, where f is defined by 

\[f(n) =   \begin{cases}     x^3-3,       & \quad \text{if } x {\leq 2}\\     x^2+1,  & \quad \text{if } x \text{>2}   \end{cases}\]

Solve system of linear equations, using matrix method.
 2x+3y+3z=5
 x-2y+z=-4
 3x-y-2z=3

Find all points of discontinuity of f, where f is defined by 

\[f(x) =   \begin{cases}     x+1,       & \quad \text{if } x{\geq1}\\    x^2+1,  & \quad \text{if } x \text{<1}   \end{cases}\]

Solve system of linear equations, using matrix method.
x-y+z=4
2x+y-3z=0 
x+y+z=2

Find all points of discontinuity of f,where f is defined by 

\[f(x) =   \begin{cases}     \frac {x}{|x|},       & \quad \text{if } x \text{<0}\\     -1,  & \quad \text{if } x {\geq 0}   \end{cases}\]

Solve system of linear equations, using matrix method.
2x+y+z=1
x-2y-z=\(\frac{3}{2}\)
3y-5z=9

Find all points of discontinuity of f,where f is defined by 

\[f(x) =   \begin{cases}    \frac {|x|} {x},      & \quad \text{if } x { \neq 0}\\     0,  & \quad \text{if } x { =0}   \end{cases}\]
Appearance of male secondary characters in females is

Find all points of discontinuity of f,where f is defined by 

\[f(x) =   \begin{cases}     |x|+3,      & \quad \text{if } x\  {\leq-3}\\     -2,  & \quad \text{if } -3<x<3 \text{} \\ 6x+2, & \quad \text{if } x\  {\geq 3}  \end{cases}\]

Find all points of discontinuity of f, where f is defined by 

\[f(x) =   \begin{cases}     2x+3,      & \quad \text{if } x {\leq 2}\\     2x-3,  & \quad \text{if } x \text{>2}   \end{cases}\]

Solve system of linear equations, using matrix method.
 5x+2y=3
 3x+2y=5

Solve system of linear equations, using matrix method.
4x-3y=3
3x-5y=7

Is the function f defined by

\[f(x) =   \begin{cases}     x,      & \quad \text{if } n{\leq1}\\    5,  & \quad \text{if } n{ >1}   \end{cases}\]

continuous at x=0? At x=1? At x=2?

Prove that the function f(x) = xn, is continuous at x = n, where n is a positive integer.

Solve system of linear equations, using matrix method.
  2x-y=-2
  3x+4y=3

Solve system of linear equations, using matrix method.
 5x+2y=4,
 7x+3y=5

Examine the consistency of the system of equations.
 5x−y+4z=5,
 2x+3y+5z=2,
 5x−2y+6z=−1

Examine the consistency of the system of equations.
 3x-y−2z=2,
 2y−z=−1
 3x−5y=3

Examine the consistency of the system of equations.
x+y+z=12x+3y+2z=2,
ax+ay+2az=4

Examine the consistency of the system of equations.
x+3y=5,
2x+6y=8

If \(A = \begin{bmatrix}        \frac{2}{3} & 1 & \frac 53           \\[0.3em]        \frac{1}{3} & \frac 23           & \frac{4}{3} \\[0.3em]        \frac 73           & 2 & \frac{2}{3}      \end{bmatrix}\) and \(B = \begin{bmatrix}        \frac{2}{5} & \frac 35 & 1           \\[0.3em]        \frac{1}{5} & \frac 25           & \frac{4}{5} \\[0.3em]        \frac 75           & \frac 65 & \frac{2}{5}      \end{bmatrix}\) then compute 3A-5B.

Examine the consistency of the system of equations.
2x-y=5,
x+y=4

Examine the consistency of the system of equations. 
x+2y=2,
2x+3y=3

Let A be a nonsingular square matrix of order 3×3.Then IadjAI is equal to