Reference no: EM13240843
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 7x2 = 2x+1 for x.
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