1.

Compute the following quantities.

1. 1111 ?345.

2. e ¹⁴ and 382801 ? to 15 digits each. Which is bigger?

3. the fractions 2709/1024, 10583/4000, and 2024/765. Which of these is the best approximation to ?

2.

Compute to 15 digits the following quantities.

1. cosh(0.1).

2. ln(2). ( Hint: the natural logarithm in MATLAB is called log, not ln.)

3. arctan(1/2). ( Hint: the inverse tangent function in MATLAB is called atan, not arctan.)

3.

Solve (symbolically) the system of linear equations

Check your answer using matrix multiplication.

4.

Try to solve (symbolically) the system of linear equations

What happens? Can you see why? Again check your answer using matrix multiplication. Is the answer correct ?

5.

Factor the polynomial x ⁴ ? y ⁴.

6.

Use simplify or simple to simplify the following expressions:

1. ,

2. cos ² x ? sin ² x.

7.

Compute 3 ³⁰¹, both as an approximate floating-point number and as an exact integer (written in usual decimal notation).

8.

Use either solve or fzero, as appropriate, to solve the following equations.

1. 67 x + 32 = 0 (exact solution).

2. 67 x + 32 = 0 (numerical solution to 15 places).

3. x ³ + px + q = 0. (Solve for x in terms of