Description

Mathematica
Problem Sheet 2
Algebraic Computation: Basic Algebra & Formula Manipulation
1. Write down the following algebraic expressions in mathematica:
a) sin 3 x b) sin cos1 x c) tanelncot1x
 2 

2. Find the value of the expression 1a) by replacing x by (Use function ReplaceAll[])
4
3. a) Write down the expression: ln x2
b) Simplify the expression under condition: x0 [Use function Simplify[]]
4. a) Write down the expression: ln ex
b) Simplify the expression under condition: xR
5. a) Write down the expression: sin2n1 
 2 
b) Simplify the expression under condition: n Z
6. a) Write down the expression: cotsin1 costan1 eln x
b) Simplify the expression under condition: x0
7. a) Write down the expression: sin2xcos x 1  2  cosec17xsec8x
 2  b) Simplify the expression
8. Simplify the expression: under condition x 0, y  0,z  0
9. Factorize the following expressions: (Use function Factor[])
a) x2 5x 6 b) ab3 a3bbc3 b3cca3 c3a
10. Expand the following expressions: (Use function Expand[])
a) ab2 b) (ab)7
11. Express the following fraction as a linear combination of partial fractions: (Use function Apart[])
x5 7x5

x22x2 3x2
12. Express the following combination of fractions as a single fraction: (Use function Together[])
1 x x x12 3×2 5x2
13. Cancel out the common factors of numerator and denominator from the given function: (Use function Cancel[])
x2 1

3 1
x 