NAME :

PHYSICS 4A ----QUIZ 0

1. You have a right triangle whose hypotenuse is of length A and one angle is given as q . Find the length of the other two sides B and C in terms of A and q .

Answer : B = cosq and C=sin q (The angle q was supposed to be between sides A and B. I forgot to put this in the diagram).

2. You know that sinq =1/2. Without using a calculator find cosq .

Answer : cos q =Ö (1-sin^2q ) = Ö (1-0.25)=Ö .75=0.866

3. Assuming that a,b,c are known constants solve for x in the equation

(a/x)+b = (c/x).

Answer : a+ b x = c à bx = c-a à x = (c-a)/b

4. What does ln(e^2.67) equal ? (don't use your calculator)

Answer : It equals 2.67 (ln "eats" e).

5. Solve the system of equations for x and y ?

3x +5y =14

-x -6y = -9

Answer : x=3 ; y = 1

6. Find the derivative (df/dx) for

(a) f(x) = a + bÖ x +c e^-x

(b) f(x) = a cos (bx²)

(a) df/dx = b/(2 Ö x) - c e^-x

(b) df/dx = -2ab x sin (bx²)

7. Find the integral (ò f(x) dx) for the functions below

1. f(x) = b x³
2. f(x) = a sin(bx +c)

Answer : (a) ò f(x) dx = (b/4) x⁴

(b) ò f(x) dx = -(a/b) cos (bx +c)

1. For the function y(x) = x(1-x² ) find

1. The maximum of this function
2. The area under the curve between the two points where it crosses the x-axis.

Answer : (a) dy / dx = 1 - 3 x² = 0 à x_max=1/Ö 3=.0577

2. y=0 at x=0 and x=1 (also it crosses at x=-1 which I didn't consider)

so ò ₀¹ x(1-x²) dx = (1/2) x² - (1/4) x⁴ |₀¹ = (1/2) - (1/4) - 0 +0 = 1/4 =0.25