CPI 200
Midterm prep / not graded

1.  Let 
	f(x) =  (Sqrt[x]) + x

Sketch f and f ’ over [0,3].

f[x_]:=Sqrt[x] +x;
Plot[{f[x],f'[x]},{x,0,3}]

2.  What is the area under f when f(x) = sin(x) and x∈[-3,3]

0 by symmetry of the sin function.

3. What is the action of the matrix

M = (({{1, 0}, {0, -1}}))

It flips across the x-axis.

4. Let

A = (({{1, 1, 0}, {1, 1, 0}, {2, -2, 1}}))  and b=(({{1}, {-1}, {0}})).

Compute A·b   (0,0,4)


5. A 2D square is mapped by an affine map to what:
a) a rectangle, b) an ellipse, c) a parallelogram. Explain.

c). Parallel lines (such as the rectangle edges) are mapped to
parallel lines.

6. What is the limit of ((3(i^2)+2)/(i!)) as i →∞?

0 since i! grows much faster than x^2.

7. Find the decimal form of the binary number 100.1

4.5

8. Let L be a line through (0,2) and (2,0). What is the distance of the point
    (1,1) to L?
    
    0 since (1,1) is on the line.
    
9. What does it mean if the dot product of two vectors is zero?

They are perpendicular.