SHEET 9

Q1. Define rational numbers.

Q2. Define irrational numbers.

Q3. Give 3 examples for irrational numbers.

Q4. Compute the following:

(1+1/n)^n

when n = 10

n = 100

n = 1000

n = 10000

n = 100000

Q5. Develop a function such that the slope of the tangent at any point is equal to the value of the function at this point.

- Write the equation for this function, then draw it, and illustrate graphically the above condition.

Q6. Solve the following differential equation

dy/dx = a y

where a is a constant.

Q7. Integrate 1/x from 1 to a.

where a is a constant (bigger than 1)

Q8. Explain why the number 'e' is specifically chosen as the base for the natural logarithm.

Q9. Generate ten samples (variates) from the Weibull distribution.

(assume that all parameters of the distribution equal one).

Here are the Us:

0.95, 0.02, 0.60, 0.44, 0.93, 0.86, 0.42, 0.19, 0.35, 0.94

Q10. Solve question 4.1 in the book (pages 107 & 108).