Assignment SM015

Chapter 01:

Number System

https://youtu.be/8RasCV_Lggg

Chapter 04:

Matrices And System of Linear Equations

1. Compute the inverse of a non singular matrix using Adjoint Matrix or ERO.

2. Solve the unique solution of AX=B using Inverse Matrix or Elimination Method.

https://youtu.be/xfhzwNkMNg4

https://youtu.be/HwRRdG_E4Yo

https://youtu.be/woqq3Sls1d8

https://youtu.be/UhhfKXBnnEo

1. Sketch the graph of a function

    * polynomials up to degree 3,

    * piecewise

    * absolute values of linear functions

    * reciprocal

    * square root with linear expression

2. Show whether a function has an inverse and find the inverse of the function.

3. Compute the inverse of a function.

4. Sketch the graph of the function f and its inverse  on the same axes.

5. Compute the composite functions involving exponential and logarithmic functions.

6. Sketch the graph which involve exponential and logarithmic functions on the same axes.

https://youtu.be/tfF_-Db8iSA

https://youtu.be/_GyVtObKsWs

https://youtu.be/W84lObmOp8M

https://youtu.be/87Duk_ySbto

https://youtu.be/9SOSfRNCQZQ

https://youtu.be/DuYgVVU_BwY

1. Construct partial fractions decomposition.

2. Change the rational polinomials to proper fraction when the degree of the numerator is the same or more than the denominator and then determine the partial fractions.

1. Use special angles. (Show by using right-angled triangle)

2. Solve the basic trigonometric equations.

    * sin x = k, cos x = k, tan x = k

3.  Solve trigonometric equations in quadratic form.

4.  Solve trigonometric equations by t substitution.

5.  Solve trigonometric equations using R sin (x+α)

6. Determine the maximum and minimum values of trigonometric expression.

Chapter 08:  Limits and Continuity

1. Determine the existence of the limit of a function.

2. Compute the vertical and horizontal asymptotes.

3.  Compute the continuity of a function at a point.