Write out the form of the partial fraction decomposition of

Question

Questions:

1. The two quadratics x² - 2qx - 6 and x² - 8x + 9q both have the same remainder when divided by x + 3. Find the value of q.

2. Factorise ?rst and then solve the equation 3x³ - 7x² - 7x + 3 = 0.

3. Consider the rational function x² - x + 6 / x³ + 3x

(a) Write out the form of the partial fraction decomposition of the function.

(b) Determine the numerical values of the coefficients.

4. Is the function f(x) = 3x³ + 2x² + 1 even, odd, or neither? Please justify your reasoning.

5. Find the domain of each of the functions:

f(x) = t²/t+2         g(x) = √1-x² /7x

6. When a camera ?ash goes off, the batteries immediately begin to recharge the ?ash's capacitor, which stores electric charge given by

(The maximum charge capacity is Q and t is measured in seconds.)

(a) Find the inverse of this function and explain its meaning.

(b) How long does it take to recharge the capacitor to 90% of capacity if a = 2

7. Consider two trigonometric functions y = cos 2x and y = 1 + sinx.

(a) Write down the equation in x that you would solve to ?nd the x coordinate of point(s) of intersection of those graphs on [0, 2π].

(b) Solve your equation, and write down the coordinates of the points of intersection .

8. Solve the equation 7^x2 = 2^x+1 for x.